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\ 'V 


I 


THE 

YOUNG MILL-WRIGHT 


AND 




’S GUIDE; 


ILLUSTRATED BY 




€iUBBtt(-(gigtit Dmriptitn n. 

BY 

OLIVER EVANS. 

%4 


&II 


BY 

THOMAS P. JONES. 

$ 

MEMBER OF THE AMERICAN PHILOSOPHICAL SOCIETY, AND LATE PROFESSOR 
OF MECHANICS IN THE FRANKLIN INSTITUTE OF PHILADELPHIA. 


WITH .s ;• i 

A DESCRIPTION OF AN IMPROVED MERCHANT FLOUR-MILL, 

Ulitl) Gntgrauings. 

BY C. & O. EVANS, ENGINEERS. 

« 

FOURTEENTH EDITION. 


<* 


PHILADELPHIA: 

BLANCHARD AND LEA. 

1853 . 


r* 











Entered, according to the Act of Congress, in the year 1834, by Carey, Lea & 
Blanchard, in the Clerk’s Office of the Eastern District of Pennsylvania. 


Jfer transfer 

JUN 84 I9ff 



VVM. S. YOUNG, PRINTER. 








PREFACE. 


There are few men whose mechanical inventions have 
contributed so much to the good of our country as those 
of Oliver Evans; for my own part, I could name but.two, 
and they are Whitney and Fulton. There have, it is 
true, within the last thirty years, been a great number of 
original machines invented, and a great many improve¬ 
ments made on those for which we are indebted to other 
countries, that do great credit to American genius, and 
evince a peculiar aptitude to excel in mechanical con¬ 
trivances ; but few, however, of these inventions could be 
denominated national, although they have been of high 
importance in the various arts to which they are applied. 

The improvements in the flour mill, like the invention 
of the cotton gin, apply to one of the great staples of our 
country; and although nearly forty years have elapsed 
since Mr. Evans first made his improvements known to 
the world in the present work, the general superiority of 
American mills to those even of Great Britain, is still a 
subject of remark by intelligent travellers. Mr. Evans, 
however, experienced the fate of most other meritorious 
inventors; the combined powers of prejudice and of in¬ 
terest deprived him of all benefit from his labours, and, 
like Whitney, he was compelled to depend upon other 
pursuits for the means of establishing himself in the 
world. His reward, as an inventor, was a long-continued 
course of ruinous litigation, and the eventual success of 
the powerful phalanx which was in league against him. 

It is not the intention of the editor to pronounce a 




IV 


PREFACE. 


panegyric on, or to write the history of, Oliver Evans; 
but his sense of justice, and a confident hope that, in 
the history of American inventions, posterity may ac¬ 
cord to him the place which he really merits, have 
called forth the preceding remarks. 

Mr. Evans made no pretensions to literature; he con¬ 
sidered himself, as he really was, a plain, practical man; 
and the main object of his writing this work was to in¬ 
troduce his inventions to public notice: it has, however, 
been extensively useful to the mill-wright and the miller, 
as a general treatise, and an edition of it has been pub¬ 
lished in the French language. The present editor was 
employed to revise the work, a few years ago, and a new 
edition being again called for, the same task has been 
again assigned to him by the publishers. It has not 
been thought proper to make any such alterations in it 
as should destroy its identity; as it would, in that case, 
be essentially a new work, to which it would not be 
proper to attach the name of Mr. Evans as the author: 
encouraged, however, by the general approval of the 
alterations and additions formerly made, the editor has 
thought himself justified in pursuing, in the present in¬ 
stance, the same course, to a greater extent; and although 
some theoretical views are interwoven in the general 
texture of the work which may be disputable, these can 
detract but little from its practical utility; and it is hoped 
that the farther changes which have been made in the 
phraseology, as well as in some other points, will be 
found to add to its worth in this respect. 

THOMAS P. JONES. 


City of Washington, April, 1834. 


CONTENTS. 


PART I. 

PRINCIPLES OF MECHANICS AND HYDRAULICS 


ARTICLE. 

1. Preliminary Remarks, ..... 

2. On the essential properties of bodies, . 

3. Axioms, or laws of motion and rest, 

4. On absolute and relative motion, 

5. On momentum, ...... 

6. On power, or force, and on the motive powers, 

7. On the effect of collision, or impact, 

8. On compound motion, ..... 

9. Of non-elasticity, and of fluidity in impinging bodies, 

10. Of falling bodies, ..... 

11. Of bodies descending inclined planes and curved surfaces, 

12. Of the motion of projectiles, .... 

13. Of circular motion and central forces, 

14. Of the centres of magnitude, motion and gravity, 

15. Of the mechanical powers, ..... 

16. Of the lever, ...... 

17. General rules for computing the power of an engine, 

18. Of the different kinds of levers, 

19. Compound levers, ...... 

20. Calculating the power of wheel-work, . 

21. Power decreases as motion increases, 

22. No power gained by enlarging undershot water-wheels, 

23. No power gained by double gearing, 

24. Of the pulley, ...... 

25. Of the wheel and axle, ..... 

26. Of the inclined plane, ..... 

27. Of the wedge, ...... 

28. Of the screw, ...... 

29. Of the fly-wheel and its use, .... 

30. On friction, ...... 

31. On the friction of different substances, 

32. Mechanical contrivances to reduce friction, 

33. Of maximums, ...... 

34. Investigation of old theory, .... 

35. New theory doubted, . . . . . 

36. True theory attempted, .... 

37. Scale of experiments, . . . . . 

38. Waring’s theory, ..... 

39. The same continued, .... 


PAGE. 

. 17 
18 

. 21 

22 
. 23 
24 
. 24 
26 
. 29 
29 
. 33 
34 
. 35 
38 
. 39 
40 
. 41 
42 
. 43 
45 
. 46 
47 
. 48 

49 
. 49 

50 
. 50 

51 
. 52 

53 
. 55 
56 
. 58 
59 
. 63 
63 
. 65 
67 
. 70 









VI 


CONTENTS. 


ARTICLE. 

40. Doubts respecting it, .... 

41. True theory farther sought for, 

42. u 11 deduced, ..... 

43. Finding the velocity of a wheel, theorem for, 

44. Maximum velocity of overshot wheels, 

Table of velocities of do, 

Preliminary remarks on hydraulics, 

45. Of spouting fluids, ..... 

46. Seventh law of spouting fluids demonstrated, 

47. Its accordance with practice shown, 

48. Hydrostatic paradox, ..... 

49. Practical results of equal pressure, 

50. To find the pressure on a vessel, .... 

51. To find the velocity of spouting fluids, 

52. Effect of water under a given head, 

53. Water applied to act by gravity, 

54. Principles of overshot mills, .... 

55. Friction of spouting fluids on apertures, 

56. Pressure of the air on fluids, .... 

57. Of pumps, ...... 

58. Conveying water under valleys and over hills, 

59. Definite and indefinite quantities of water striking a wheel, 

60. Motion of breast and pitch-back wheels, . 

61. Calculating the power of a mill seat, . 

62. Theoiy and practice compared, .... 

63. Observations and experiments on mills in practice, 

Table of the area and power of mill stones, 

64. On canals for conveying water to mills, 

65. On their size and fall, ..... 
66- Of air pipes, to prevent trunks from bursting, . 

67. Smeaton 7 s experiments concerning undershot wheels, 

68- 11 u 11 overshot wheels, . 

69. u Xi u wind mills, 


PAGE. 

. 71 
72 
. 79 
81 

. 82 
83 
. 87 
88 

. 91 
92 
. 95 

96 
. 96 

97 
. 97 

. 99 
. 101 
104 
. 105 
106 
. 108 
108 
. 110 
113 
. 115 
119 
. 125 
126 
. 127 
129 
. 130 
147 
. 155 


PART II. 


OF THE DIFFERENT KINDS OF MILLS. 


70. Of undershot mills, with a table of their proportions and powers, . 

71. Of tub-mills, with a similar table, .... 

72. Of breast and pitch-back wheels, with a table for them, . 

73. Of overshot wheels, with tables, .... 

74. Rules and calculations in regulating the motion, . 

75. Rules for finding the pitch circles, .... 

76. The same subject, with a table, . 

77. Measuring the contents of garners, hoppers, &c., 

78. Of the different kinds of gears, and forms of cogs, 

79. Of spur gears, ....... 

80. Of face gears, ••..... 

81. Of bevel gears, ....... 

82. Of matching wheels to make the cogs wear equally, 

83. Of rolling screens and fans, ..... 

84. Of gudgeons, preventing their heating, &c. ; 

85. Building mill dams, . . . 

86. Building mill walls, . 


161 

162 

177 

179 

185 

188 

189 

193 

195 

195 

197 

199 

201 

202 

204 

207 

209 









CONTENTS. 


• • 
Vll 


PART III. 


DESCRIPTION OF THE AUTHOR’S IMPROVEMENTS. 


ARTICLE. 

87. General account of the author’s improvements, . 

88. Of the elevator, conveyer, hopper-boy, drill and descender, 

89. Application of the machines in manufacturing flour, 

90. Elevating grain from snips, .... 

91. A mill for grinding parcels, .... 

92. Improved grist mill, ..... 

93. On elevating from ships, &c., by horse power, . 

94. On the same, by manual power, 

95. Particular directions for constructing elevators, &c., 

96. Of the meal elevator, ..... 

97. u meal conveyer, ..... 

98. 11 grain conveyer, .... 

99. u hopper-boy, ..... 

100. “ drill, ...... 

101. Utility of these machines, .... 

102. Bills of materials for their construction, 

103. Mill for hulling and cleaning rice, 


PAGE. 
. 211 
212 
. 216 
219 
. 221 
223 
. 225 
226 
. 229 
237 
. 239 
241 
. 242 
244 
. 246 
248 
. 251 


PART IY. 


ON THE MANUFACTURE OF GRAIN INTO FLOUR. 


104. Explanation of the principle of grinding, . 

105. Of the draught necessary to be given to the furrows of mill-stones, 

106. Of facing mill-stones, ...... 

107. Of hanging u ...... 

108. Of regulating the feed and water in grinding, 

109. Rules for judging of good grinding, . 

110. Of dressing and sharpening the stones when dull, 

111. Of the most proper degree of fineness for flour, . 

112. Directions for grinding wheat mixed with garlic, &c., 

113. Of grinding middlings over, &c., . 

114. Of the quality of mill-stones to suit that of the wheat, 

115. Of bolting reels and cloths, with directions for bolting and in¬ 

specting floor, . . . . . . • 

116. The duty of the miller, . 

117. Peculiar accidents by which mills are subject to catch fire, . 

118. Observations pn improving mills, . 


255 

258 

262 

263 

266 

267 

268 

269 

270 

271 
275 

277 

280 

282 

283 


PART Y. 

ellicott’s plans for building mills. 

Prefatory remarks, ..... 

119. Undershot mills, and laying on the water, 

120. Directions for making forebays, . 

121. Principle of undershot mills, .... 

122. Of breast wheels, ..... 

123. Of pitch-back wheels, .... 

124. Of overshot wheels, .... 

125. Of the motion of overshot wheels, 

126. Of gearing, ..... 

127. Diameter of pitch circles, .... 


285 

288 

289 

290 

293 

294 

294 

295 

296 

297 





CONTENTS. 


Vlll 


ARTICLE. 

128. 

129. 

130. 

131. 

132. 

133. 

134. 

135. 

136. 

137. 

138. 

139. 

140. 

141. 

142. 

143. 

144. 

145. 

146. 

147. 

148. 

149. 

150. 

151. 

152. 

153. 

154. 

155. 

156. 

157. 

158. 

. 159. 

160. 

161. 


u 

a 

a 


Table for overshot mills of different falls, &c. &c., 
Constructing undershot wheels, .... 

Dressing shafts, ...... 

Directions for laying out mortises for arms, . 
for putting in gudgeons, 
for constructing cog-wheels, 
for making sills, spurs, and head blocks, 

Of the best time for cutting, and method of seasoning, cogs, 
Of shanking, putting in, and dressing off cogs, 

Of the little cog wheel and shaft, .... 

Directions for making wallowers and trundles, . 

for fixing the head blocks and hanging the wheels, 
for sinking the balance ryne, . 
for bridging the spindle, .... 

for making the crane and lighter-staff, 
for making a hoop for the mill-stones, 
for grinding sand to face the stones, . 
for laying out the furrows in new stones, 
for making a hopper, shoe and feeder, 
for making bolting chests and reels, 
for setting bolts to go by water, 
for making bolting wheels, 

Of rolling screens, ..... 

Of fans, ....... 

Of the shaking sieve, ..... 

Of the use of draughting to build mills by, 

Directions for draughting and planning mills, 

Bills of scantling for a mill, ..... 

Bills of iron work for a mill, .... 

Explanation of the plates, ..... 

Of saw-mills, with a table of the dimensions of flutter-wheels, 
Of fulling-mills, ...... 

Management of the saw-mill, .... 

Mr. French on saw-mills, &c., .... 

Rules for discovering new improvements, 


u 

(C 

u 

a 

u 

u 

u 

(( 

u 

u 

u 


PAOE. 
. 299 
304 
. 306 
306 
. 308 
309 
. 311 
312 
. 312 

314 
. 314 

315 
. 316 

317 
. 317 

318 
. 319 

320 
. 321 
322 
. 323 
324 
. 326 
327 
. 327 
329 
. 330 
331 
. 334 
336 
. 340 
348 
. 350 
355 
. 352 


APPENDIX. 

Description of an improved merchant-mill, . . . 365 

On the construction of water-wheels, by W. Parkin, &c., . 370 

Remarks by the editor, ..... 373 

On the distance which bodies fall, and the velocities acquired in 

consecutive periods of time, with a table, . . 374 

Comparison of different water-wheels, by Mr. Perkins and Mr. 

Manwaring, ...... 377 * 

Remarks, by the editor, . . . . . .379 


EXTRACTS FROM BUCHANAN ON MILL-WORK. 

Strength and durability of the teeth of wheels, 

Of arranging the numbers of “ . . 

Of making patterns for cast iron, . 

Of malleable or wrought iron gudgeons, 

Of the bearings of shafts, . 

On the framing of mill-work, .... 

On reaction wheels, (extracted from Franklin Journal,) . 
Definition of terms, ..... 


380 

385 

386 

389 

390 

391 

392 
396 



Jf Oepart^ e 


£/brab^ 



THE 


YOUNG MILL-WRIGHT 

AND 

MILLER’S GUIDE. 


^nrt ijjt /irst. 


CHAPTER I. 

MECHANICS. 

OF THE GENERAL PROPERTIES OF BODIES AND THE FIRST PRIN¬ 
CIPLES OF MECHANICS. 

ARTICLE 1. 

« 

PRELIMINARY REMARKS. 

Although there are many good, practical workmen 
who are entirely ignorant of the theory of mechanics as 
a science, it will be universally acknowledged that an 
acquaintance with the general properties of matter and 
the laws of motion would not only be gratifying to every 
intelligent mind, but would introduce a certainty into 
many mechanical operations which would ensure their 
success; and this is a truth, with the importance of which 
the author of this work was so fully impressed, that he 
devoted a whole chapter to its consideration. The pre¬ 
sent editor has thought it best to alter and modify the 
original work, but he has been careful not only to retain 
all that appeared to him important in it, but to make 
such additions, and give such an arrangmentto the whole, 
as have appeared to him calculated to place the subjects 
of which it treats in a more familiar light. 

2 








18 


MECHANICS. 


[CHAP. I. 

It is only, however, those properties of bodies, and 
those laws of motion, which most intimately concern 
the practical mechanician, that it is thought proper 
here to treat at any length, as any thing farther would 
be entirely foreign to the object of this work. 


ARTICLE 2. 

ON THE ESSENTIAL PROPERTIES OF BODIES. 

There are certain properties of bodies which belong 
to matter in all its forms. These are called its essential 
properties, as they are those without which it cannot 
exist: they are Extension , Figure , Impenetrability , Di¬ 
visibility , Mobility , Inertia , and Attraction. 

Extension. We become acquainted with the existence 
of matter only by the space which it occupies. We 
cannot conceive of a body without length, breadth, and 
thickness, which are the three dimensions of extension. 
These vary greatly from each other in different bodies; 
and in some they are all equal to each other, as in the 
sphere and the cube. 

Figure , or shape, is the necessary result of extension, 
and constitutes its limits. The business of the ma¬ 
chinist is to give to various substances those figures, or 
shapes, which shall adapt them to his purpose. 

Impenetrability is that property by which a body oc¬ 
cupies a certain space, which cannot, at the same time, 
be occupied by another body. If a nail be driven into 
a piece of wood, it removes a portion of the latter out 
of its way. Water and other fluids may be made to 
enter the pores of wood, but it is manifest that two dis¬ 
tinct particles of matter cannot exist in the same space 
with each other. 

Divisibility is the susceptibility of matter to be divided 
into any number of parts. If in conceiving of the minute¬ 
ness of the particles of matter, we carry the imagination 
to its utmost limits, we must confess that a single parti¬ 
cle must contain as many halves, quarters, and eighths, 
as the largest masses. We are not to conclude from this, 



MECHANICS. 


19 


CHAP. I.] 

however, that matter is actually infinitely divisible, al¬ 
though it is mathematically so. It is probable that the 
Creator has formed masses of matter of certain minute 
particles, which are infinitely hard, and incapable, from 
their nature, of mechanical division. 

Mobility is one of those essential properties of matter, 
which form the very foundation of operative mechanics, 
as it is the capability of matter to be moved from the 
place, or space, which it now occupies. No mechanical 
operation, indeed, or any other change, can be effected 
in matter without motion. 

Inertia , or inactivity, is that negative property of mat¬ 
ter by which it resists every change of state, whether of 
rest or of motion. By this term we mean to express the 
fact that matter is powerless; that if at rest, it has no¬ 
thing within itself tending to put it into motion; and if 
in motion, its own tendency is to continue to move, which 
it would consequently do perpetually, but for those ex¬ 
traneous resistances to which every thing upon the sur¬ 
face of the earth is subjected. The term vis inertia 3, or 
the power of inertia, is altogether objectionable, although 
it is very frequently employed. If inertia were a power 
existing in a body, it must be in some definite quantity, 
capable of being expressed in numbers, and of resisting 
a force less than itself; but it is a fact, that any force im¬ 
pressed, however small, will move any body, however 
great. 

Attraction is that power which exists in particles or 
in masses of matter, by which they tend to approach 
each other. It has been divided into five kinds; the at¬ 
traction of Gravitation , of Cohesion or aggregation, of 
Magnetism , of Electricity , and Chemical attraction. It 
is the two former only of these attractions which claim 
particular attention in their relationship to mechanics. 

The attraction of Cohesion is that power by which par¬ 
ticles of matter become united together and form masses. 
We could conceive of the existence of matter without at¬ 
traction, but it must be in its original constituent parti¬ 
cles only, unformed into masses: all matter, however, is 
manifestly endowed with this property, and its particles 
are, therefore, capable of being united together. In or¬ 
der that the attraction of cohesion may be exerted, it is 


20 


MECHANICS. 


[CHAP. I. 

necessary that the particles of matter be in contact with 
each other, as it does not take place at sensible dis¬ 
tances. By sawing, filing, grinding, and many other 
mechanical operations, we destroy the attraction of co¬ 
hesion; and this, indeed, is the great object of these pro¬ 
cesses. In those bodies which are capable of undergo¬ 
ing fusion, as the metals, we can readily restore this at¬ 
traction, by subjecting the disintegrated particles to this 
process. 

The attraction of Gravitation is manifested in masses as 
well as in particles of matter. By it all the bodies in na¬ 
ture tend to approach each other. The sun, the earth, 
the moon, and all the planets, notwithstanding their im¬ 
mense distances, are subjected to this universal law. A 
stone, or other substance, if unsupported, falls to the 
earth in consequence of the attraction existing between 
it and the earth. What we call weight, results from 
this attraction, and is the measure of its force or 
power, in different bodies. The weight of a body is the 
sum of the attractive force exerted upon its individual 
particles. A piece of lead, weighing two pounds, con¬ 
tains twice as many particles as another weighing but 
one pound, and it is therefore drawn to the earth with 
double the force. It might be supposed that, in conse¬ 
quence of this double quantity of attraction, the piece of 
two pounds would fall with double the velocity of that 
of one pound; but, upon making the experiment, the 
time of their fall will be precisely the same in each. 
This arises from the inertia of matter, by which, when at 
rest, it tends to remain so; and, therefore, to move a 
double quantity with the same velocity, must require a 
double force. Gravitation must be considered as act¬ 
ing equally on each particle, and consequently, there ex¬ 
ists no reason why a piece weighing two pounds should 
fall with any greater rapidity than would its two halves, 
were it divided. Light bodies, which expose a large 
surface to the air, are retarded in their fall by the resist¬ 
ance which it presents; were that removed, a feather 
would fall with the same velocity as a piece of lead. 

This fact is of high importance in practical mechanics, 
as, in the greater number of instances, gravitation is the 


MECHANICS. 


21 


CHAP. I.] 

active agent in moving machines, and in the construc¬ 
tion of all it is an element which must enter into the 
calculation of their power. 


ARTICLE 3. 

AXIOMS, OR LAWS, OF MOTION AND REST. 

1. Every body in a state of rest will remain so; and 
every body in motion will continue to move in a right 
line, until a change is effected by the agency of some 
mechanical force. 

2. The change from rest to motion, and from motion 
to rest, is always proportional to the force producing 
these changes. 

3. Action and reaction are always equal, and in direc¬ 
tions contrary to each other; or, when two bodies act 
upon each other, the forces are always equal, and di¬ 
rected towards contrary parts. 

The first of these laws results, necessarily, from the 
inertia of matter. The assertion, however, that a body 
in motion would continue to move in a right line, may 
require some illustration. That motion when once com¬ 
municated would never cease, is fairly inferred from the 
fact that the motion is continued in the exact proportion 
in which the obstruction is diminished. A pendulum 
will vibrate longer in air than in water, and longer still 
in an exhausted receiver, and stops at last in consequence 
of the friction on its points of suspension, and the imper¬ 
fection of the vacuum. 

When a stone is thrown in a horizontal direction, as 
motion is constantly retarded, it also moves in a curve, 
and eventually falls to the ground. The retardation, in 
this case, is exactly proportioned to the density of the 
air, and the curve in which it moves is the consequence 
of the force of gravity, which is always drawing it to¬ 
wards the earth: the curve in which it moves is deter¬ 
mined by this known force, and is precisely proportion¬ 
ate to it. It necessarily follows, that, if the course of 
retardation and of deflection were both removed, the 



22 


MECHANICS. 


[ciiap. i. 

body would continue its course in a right line. The pre¬ 
ceding remarks may serve to illustrate the second, as 
well as the first law. 

The third law is confirmed by all our observations on 
the motions of the heavenly bodies, and by all our expe¬ 
riments. If a glass bottle be struck by a hammer, or a 
hammer by a glass bottle, the bottle will in either case be 
broken by the same degree of moving power: were the 
hammer equally fragile with the bottle, both would be 
broken. If a stone be thrown against a pane of glass, the 
glass would be broken and the stone retarded, in exact 
proportion to the resistance offered by the glass. 

To assert the contrary of this law would be to main¬ 
tain an absurdity; for if action and reaction be not equal, 
one must be greater than the other, which would be to 
say that the effect w^as greater than, or not equal to the 
cause. 


ARTICLE 4. 

AN ABSOLUTE AND RELATIVE MOTION. 

The idea intended to be conveyed by the term motions 
is too familiar to require a definition. 

Motion is either absolute or relative. 

Absolute motion is the removal of a body from one part 
of space to another, as the motion of the earth in its 
orbit. 

Relative motion is the change of place which one body 
undergoes in relationship to another; such, for example, 
as the difference of motion in the flight of two birds, or 
the sailing of two ships. 

Were all the articles upon the surface of the earth to 
retain their respective situations, they would still be in 
absolute motion with the earth in space, but they would 
experience no relative motion, and would appear to us 
to be at rest. 

In the theory of mechanics, much information is de¬ 
rived from our knowledge of the laws observed by the 
heavenly bodies in their absolute motions; but, in prac- 



MECHANICS. 


23 


CHAP. I.] 

tical mechanics, we have to do with relative motion 
only. 

On equable , accelerated , and retarded motion. 

* Time must, of necessity, enter into the idea of motion, 
as it is the measure of its velocity. Thus a body which 
passes the distance of two miles in an hour, moves with 
twice the velocity of another, which, in the same time, 
travels but one mile. 

A body in motion may continue to move with the 
same velocity throughout its whole course; its motion 
is then said to be equable; or, 

Its motion may be perpetually increasing, as is the 
case with falling bodies. This is denominated accele¬ 
rated motion. 

Retarded motion is that which is continually de¬ 
creasing; such is the motion of a stone, or of a cannon 
ball, projected perpendicularly upwards. 

The cause of the equable acceleration of falling 
bodies, and the retardation of such as are projected up¬ 
wards from the earth, will be rendered clear, by attend¬ 
ing to the article on falling bodies. 


ARTICLE 5. 

OF MOMENTUM. 

It is known to every one that if the velocity of a 
moving body be increased, the force with which it will 
strike against another body will be increased also: the 
fact is equally familiar, that if the weight of a body in 
motion be increased, the result will be similar. It is 
evident, therefore, that the force with which a body in 
motion strikes against another body, must be in the 
compound ratio of its velocity, and its mass or quantity 
of matter. This force is called its momentum , which is 
the product of its quantity of matter multiplied by its 
quantity of motion; or, in other words, its weight multi¬ 
plied by its velocity. 



24 


MECHANICS. 


[CHAP. I. 

The effects produced by the collision of bodies against 
each other differ greatly in those which are elastic, from 
those that are non-elastic, which will be more particu¬ 
larly noticed presently. 


ARTICLE 6. 

ON POWER OR FORCE AND ON TIIE MOTIVE POWERS. 

Force , or power, in a mechanical sense, is that which 
causes a change in the state of a body, from motion to 
rest, or from rest to motion. 

When two or more forces act upon a body, in such a 
way as to destroy the operation of each other, there is 
then said to be an equilibrium of forces. 

The Motive Powers are those which we employ to pro- 
• duce motion in machines. These are: the strength of 
men, and of other animals; the descent of weights; the 
force of water in motion; wind, or the motion of the 
air; the elasticity of springs, and the elastic force of 
steam. The whole of these are included in the two 
principles of Gravitation and Elasticity. 

Attempts have been made to employ other agents as 
motive powers, but these have either failed altogether, 
or have not been attended with that success which justi¬ 
fies the giving to them a place in a practical work. 
Among these may be mentioned magnetism; electricity; 
condensed air; air rendered more elastic by heating it; 
explosive gases and fulminating compounds. 


ARTICLE 7. 

ON THE EFFECTS OF COLLISION, OR IMPACT. 

The striking of bodies against each other is denomi¬ 
nated collision, or impact. 

Bodies are divided into elastic and non-elastic. By 
elastic bodies are intended those which resume their di- 






MECHANICS. 


25 


CHAP. I.] 

mensions and form, when the force which changes them 
is removed. Non-elastic bodies are those which not only 
change their forms when struck, hut remain perma¬ 
nently altered in this particular. Although there are 
no solid bodies which possess either of these properties in 
perfection, yet the difference between those which are 
most, and those which are least elastic, is sufficiently 
great to justify the division. 

Ivory and hardened steel are eminently elastic. Such 
bodies, when struck together become flattened at the 
point of contact; but immediately resuming their form, 
they react upon each other, and rebound. Lead and 
soft clay are non-elastic: if two balls of either of these 
substances be struck together, a permanent flattening 
is produced at their points of contact, and they do not 
rebound. 

If two non-elastic bodies, A and B, fig. 1, each having 
the same quantity of matter, move towards each other 
with equal velocities, they will come into contact, as at 
A B, in the centre, where they will remain at rest after 
the stroke, because their momentums were equal, and 
in opposite directions. That is, if each have two pounds 
of matter, and a velocity which we may call ten, the 
momentum of each is twenty; and just sufficient, there¬ 
fore, to destroy each other. 

If, on the contrary, the bodies be perfectly elastic, 
they will recede from each other with the same velocity 
with which they met. In the former case a permanent 
indentation was produced on the bodies; in the present 
the flattening is instantaneous only, and the particles 
resuming their former position and arrangement, react 
upon each other with a force equal to their action, and, 
after the stroke, recede with undiminished velocity. 

If two non-elastic bodies, A and B, fig. 2, moving in 
the same direction with different velocities, impinge upon 
each other, they will move on together after the stroke 
with such velocity as being multiplied into the sum of 
their weights, will produce the sum of the momentums 
which they had before the stroke; that is, if each weigh 
one pound, and A has 3, and B 4 degrees of velocity, 
the sum of their momentum is 12; lx 8 + 1x4 = 12: 


26 


MECHANICS. 


[CHAP. I. 

then after the stroke their velocity will be 6; which, 
multiplied into their quantity of matter, 2, produces 12. 
The quantity of motion before and after the stroke, or, 
which is the same thing, their moment urns, will be un¬ 
changed. 

If, on the contrary, they had both been elastic, and 
moving as before, then, after the stroke, A would have 
moved with four, and B with eight degrees of velocity: 
they would consequently have interchanged velocities, 
but the quantity of motion would remain unchanged. 

If A and B be non-elastic bodies, equal in quantity of 
matter and moving with a velocity 10, come into con¬ 
tact with B at rest, they will move on together with the 
velocity 5. The quantity of motion will therefore re¬ 
main unchanged, a double mass moving with one half 
the velocity. If the bodies A and B be both elastic, B 
after the stroke will fly off with the velocity 10, and A 
will remain at rest. The quantity of motion will, as 
before, remain unchanged. To understand this difference 
between elastic and non-elastic bodies, we may suppose 
that when the two elastic bodies come into contact with 
each other, they tend to move on together, like the non¬ 
elastic, with one half the velocity of the body A; that 
is, A gives half its motion to B; but being elastic, the 
impinging parts, which give way, instantaneously re¬ 
sume their form, and react upon each other with a force 
equal to their first action, which drives A back with a 
velocity 5, and B forward with an equal velocity: the 
effect of which must be to leave A at rest, and to accu¬ 
mulate the whole motion in B. 


ARTICLE 8. 

ON COMPOUND MOTION. 

If a body be struck by two equal forces, in contrary 
directions, it will remain unmoved; but if the forces, in¬ 
stead of acting on the body in directions exactly oppo¬ 
site, strike it in two directions inclined to each other, 
motion will be communicated to the body so struck; but 
its direction will not be that of either of the striking bo- 



MECHANICS. 


27 


CHAP. I.] 

dies, but somewhere between them, dependent upon the 
power of the blows respectively. The motion in this 
case is manifestly compounded of the two possessed by 
the striking bodies, and is therefore called a compound 
motion. 

If a body A, fig. 4, receive two strokes, or impulses 
at the same time, in different directions, one which would 
propel it from A to B in a given time, and another 
which would propel it from A to D in an equal time, 
then this compound force will propel it from A to C, in 
the same time in which it would have arrived at B or 
D by one impulse only. If lines be drawn from C, to 
join B, and D, the parallelogram A B C D, will be 
formed, in the diagonal of which the compound motion 
was performed. If the two impulses had been equal, 
then A D would be equal to A B, and the parallelogram 
would become a square. 


ARTICLE 9. 

OF NON-ELASTICITY, AND OF FLUIDITY, IN IMPINGING BODIES. 

If A and B, fig. 3, be two columns of matter in mo¬ 
tion, meeting each other, and equal in non-elasticity, 
quantity and velocity, they will meet at the dotted line 
e e, destroy each other’s motion, and remain at rest, pro¬ 
vided none of their parts separate. 

But if A be elastic, and B non-elastic, when they meet 
at e e, B will give way by battering up, and both will 
move a little farther; that is, half the distance that B 
shortens. 

But if B be a column of fluid, and when it strikes A, 
flies off in a lateral direction, perpendicular to A, then 
whatever is the sum total of the momentums of these par¬ 
ticles laterally, has not been communicated to A. 

But with what proportion of the striking velocity the 
fluid, after the stroke, will move in the lateral direction, 
I do not find determined; but, from some experiments I 
have made, I suppose it to be more than one half; be¬ 
cause water falling four feet, and striking a horizontal 
plane with 16.2 feet velocity, will cast some few drops to 
the distance of 9 feet (say 10 feet, allowing one foot to 




28 


MECHANICS. 


[CHAP. I. 

be lost by friction, &c.) which we must suppose take 
their direction at an angle of 45 degrees; because a body 
projected at an angle of 45 degrees, will describe the 
greatest possible horizontal range. It is known also, that 
a body falling 4 feet and reflected with its acquired ve¬ 
locity 16.2 feet at 45 degrees, will reach 16 feet hori¬ 
zontal range, or four times the distance of the fall. 
Therefore, by this rule, i of 10 feet, equal to 2.5 feet, is 
the fall that will produce the velocity necessary to this 
effect, viz. velocity 12.64 feet per second, about three 
quarters of the striking velocity. 

This side force cannot be applied to produce any far¬ 
ther forward force, after it has struck the first obstacle, 
because its action and reaction then balance each other; 
which I demonstrated by fig. 27. 

Let A be an obstacle, against which the column of 
water G A, of quantity 16, with velocity per second 16, 
strikes: as it strikes A, suppose it to change its direction 
at right angles with I velocity and to strike B B, then 
to change again and strike forward against C C, and back¬ 
wards against D D; then again in the side direction 
E E; and again in the forward and backward directions, 
all of which forces counteract and balance each other. 

Therefore, if we suppose the obstacle A to be the float 
of an undershot water-wheel, the water can be of no far¬ 
ther service in propelling it, after the first impulse, but 
rather a disadvantage; because the elasticity of the float 
will cause it to rebound in a certain degree, and, instead 
of keeping fully up with the float it struck, to react back 
against the next float. It will be better, therefore, to let 
it escape freely as soon as it has fully made the stroke; 
not sooner, however, as it will require a certain space to 
act in, which will be in direct proportion to the distance 
between the floats. 

From these considerations, we may conclude, that the 
greatest effect to be obtained from striking fluid swill not 
amount to more than half the power which gives them 
motion, and much less, if they be not applied to the best 
advantage: and also that the effect produced by the col¬ 
lision of non-elastic bodies will be in proportion to their 
non-elasticity. 




CHAP. I.] 


MECHANICS. 


29 


ARTICLE 10. 

OF FALLING BODIES. 

Bodies descending freely by tlieir gravity, in vacuo, or 
in a non-resisting medium, are subject to the following 
laws:— 

1st. They are equally accelerated. 

It is evident, that, in every equal part of time, the body 
must receive an equal impulse from gravity, which will 
propel it at an equal distance, and give it an equal addi¬ 
tional velocity; it will, therefore, produce equal effects in 
equal times; and the velocity will be proportioned to the 
time. 

2d. Their velocity is always in proportion to the time 
of their fall, and the time is as the square root of the dis¬ 
tance fallen. 

If the velocity, at the end of one second, be 32.4 feet, 
at the end of two seconds, it will be 64.8; at the end of 
three seconds, 97.2 feet per second, and so on. 

3d. The spaces through which they pass are as the 
squares of the times and the velocities. 

That is, as the square of one second is to the space 
passed through, 16.2, so is the square of two seconds, 
which is 4, to 64.8 feet, passed through at the end of 2 
seconds; and so on, for any number of seconds. There¬ 
fore the spaces passed through at the end of every second 
will be as the square numbers 1, 4, 9, 16, 25, 36, &c., and 
the spaces passed through, in each second separately, 
will be as the odd numbers 1, 3, 5, 7, 9, 11, 13, 15, &c. 

4th. Their velocities are as the square root of the space 
descended through, and their force, to produce effect, as 
their distances fallen, directly. 

That is, as the square root of 4, which is 2, is to 16.2, 
the velocity acquired in falling four feet, so is the square 
root of any other distance, to the velocity acquired in fall¬ 
ing that distance. 

5th. The space passed through the first second is very 
nearly 16.2 feet, and the velocity acquired, at the lowest 
point, is 32. 4 feet, per second. 

6th. A body will pass through twice the space, in a 
horizontal direction, with the last acquired velocity of 





MECHANICS. 


30 


[cnAP. i. 


the descending body, in the same time that its fall re¬ 
quired. 

That is, suppose the body, as it arrives at the lowest 
point of its fall, and has acquired its greatest velocity, 
were to be turned in a horizontal direction, or that the ac¬ 
celeration from gravity was at that moment to cease, and 
the velocity to continue uniform, it would then pass over 
double the distance that it had descended through, in the 
same time. 

7th. The total sum of the effective impulse acting on 
falling bodies to give them velocity, is in direct propor¬ 
tion to the space descended through; * and their velocity 
being as the square root of the space descended through, 
or, which is the same, as the square root of the total im¬ 
pulse, therefore, 

8th. Their momentums, or force to produce effects, 
are as the squares of their velocities,f or directly as their 
distances fallen through; and the times expended in pro¬ 
ducing the effects are as the square root of the distance 
fallen through. 

That is, if a body fall 16 feet, and strike a non-elastic 
body, such as soft lead, clay, &c., it will strike with ve¬ 
locity 32, and produce a certain effect in a certain time. 
Again, if it fall 64 feet, it will strike with velocity 64, and 
produce a quadruple effect, in a double time; because if 
a perfectly elastic body fall 16 feet (in one second of time, 
and strike a perfectly elastic plane, with velocity 32 feet,) 
it will rise 16 feet in one second of time. Again, if the 
body fall two seconds of time, it will fall 64 feet, and 
strike with velocity 64, and rise 64 feet in two seconds 
of time. Now if we call the rising of the body the effect 
of the striking velocity (which it really is) then all will 
appear clear. I am aware that any thing here advanced, 
which is contrary to the opinion oflearned and ingenious 
authors, ought to be doubted, unless found to agree with 
practice. 


* This is evident from the consideration that in every equal part of distance 
it descends through, it receives an equally effective impulse from gravity. 
Therefore, 4 times the distance gives 4 times the effective impulse. 

f This is evident, when we consider that a quadruple distance, or impulse, 
produces only double velocity, and that a quadruple resistance will be required 
to stop double velocity; consequently, their force is as the squares of their 
velocities, which brings them to be directly as their distances descended 
through: and this agrees with the second law of spouting fluids, Art. 45. 



CHAP. I.] 


MECHANICS 


31 


A TABLE 

OF THE 

MOTION OF FALLING BODIES. 

SUPPOSED IN VACUO. 


Distance passed through 
in feet. 

The velocity acquired by 
the fall in feet and parts, 
counted per second." 

Seconds of time that a 
body is supposed to be 
falling. 

Distance passed through 
in said time, in feet 
and parts. 

Velocity per second ac¬ 
quired at the end of 
every second, in feet 
and parts. 

1 

8.1 

.125 

.25 

4. 

2 

11.4 

.25 

1.01 

8.1 

3 

14. 

.5 

4.05 

16.2 

4 

16.2 

.75 

9.11 

24.3 

5 

18. 

1 

16.2 

32.4 

6 

19.84 

2 

64.8 

64.8 

7 

21.43 

3 

145.8 

97.2 

8 

22.8 

4 

259.2 

129.6 

9 

24.3 

5 

305. 

162. 

10 

25.54 

6 

583.2 

194.4 

11 

26.73 

7 

793.8 

226.8 

12 

28. 

8 

1036.8 

259.2 

13 

29.16 

9 

1312.2 

291.6 

14 

30.2 

10 

1620. 

324. 

15 

31.34 

30 

14580. 

972. 

16 

32.4 

60 

58320. 

1944. 

17 

33.32 




18 

34.34 




19 

35.18 




20 

36.2 




21 

37.11 




36 

48.6 




49 

56.7 




64 

64.8 




100 

81. 




144 

97.2 







and parts. 











32 


MECHANICS 


[CHAP. I. 


A SCALE OF THE MOTION OF FALLING BODIES. 


4l 

X> X 

4 ) 

U 

rt <N 

2 

si 

m C 
V V 

1= 

r Jl 


1". 


5 


8 


3" . . 9 


4" . . 16- 


In this table the time is divided into 
seconds, and the absolute distances are 
proportioned to this division; but the 
ratios are the same, whether minutes, 
hours, or any other period, be taken 
as the unit of time. 


.5 rt 

~ k. >- 

r- O 

if c 
~_r;2 
5 g o 

S « 


a x 

<Z> 


0) - ^ 
o o c 

55 £.2 
02 


~~G— 

.h o 
3 « 
Cox 
o o = 

CS l_ « 

C(3 
O 01 

a o 
O-C c 
> ■“ cl 

V* 03 


— •? 
£ o 


Cfj a) 

R « 

2 1 4>S 
o rt-52 - ^'s 

_ 'n JH ~ 


o 


0^0 
w - « 
o <D 

< ® ■ 


-a. 


Velocity in feet, acquired at the end 
of 1 "= 32.4 feet. 


Velocity acquired at the end of 2' 
64.8 feet. 


Velocity acquired at the end of 3"= 
97.2 feet. 


10 


11 


12 


13 


14 


15 


feet. 

16.2 


64.8 


• • • . . . " ■. cl . 

Velocity acquired at the end of 4" = 
129.6 feet. 


145.8 


259.2 





































































MECHANICS. 


33 


CHAP. I.] 

This scale shows at one view all the laws observed by 
falling bodies. The body 0 would fall from 0 to 1, equal 
to 16.2 feet, in the first second, and acquire a velocity 
that would carry it 32.4 feet from I to a, horizontally, 
in the next second, by laws 5 and 6; this velocity would 
also carry it down to three in the same time; but its grar 
vity, producing equal effects, in equal times, will acce¬ 
lerate it so much as to take it to 4 in the same time, by 
law 1. It will now have a velocity of 64.8 feet per se¬ 
cond, that will take it to b horizontally, or down to 8, 
but gravity will help it on to 9 in the same time. Its 
velocity will now be 97.2 feet; which will take it hori¬ 
zontally to c or down to 15, but gravity will help it on 
to 16; and its last acquired velocity will be 129.6 feet, 
per second, which would carry it to cl horizontally. 

If either of these horizontal velocities be continued, 
the body will pass over double the distance it fell, in 
the same time, by law 6. 

Again, if 0 be perfectly elastic, and falling, strikes a 
perfectly elastic plane, either at 1, 3, 5, or 7, the effec¬ 
tive force of its stroke will cause it to rise again to 0 in 
the same space of time it took to fall. 

This shows, that in every equal part of distance, it 
received an equally effective impulse from gravity, and 
that the total sum of the effective impulse is as the dis¬ 
tance fallen directly—and the effective force of the 
stroke will be as the squares of the velocities, by laws 7 
and 8. 


ARTICLE 11. 

OF BODIES DESCENDING INCLINED PLANES AND CURVED SURFACES, 

Bodies descending inclined planes and curved sur¬ 
faces are subject to the following laws:— 

1. They are equably accelerated, because their motion 
is the effect of gravity. 

2. The force of gravity propelling the body A, fig. 5, 
to descend an inclined plane A D, is to the absolute gra- 



MECHANICS. 


34 


[chap. I. 


vity of the body as the height of the plane A C is to its 
length A D. 

3. The spaces descended through are as the squares 
of the times. 

4. The times in which the different planes A D, A II, 
and A I, or the altitude A C, are passed over, are as 
their lengths respectively. 

5. The velocities acquired in descending such planes, 
in the lowest points, D, H, I, or C, are all equal. 

6. The times and velocities of bodies descending 
through planes alike inclined to the horizon, are as the 
square roots of their lengths. 

7. Their velocities, in all cases, are as the square 
roots of their perpendicular descent. 

From these laws or properties of bodies descending 
inclined planes, are deduced the following corollaries, 
namely:— 

1. That the times in which a body descends through 
the diameter A C, or any chord A a, A e, or A i, are 
equal: hence, 

2. All the chords of a circle are described in equal 
times. 

3. The velocity acquired in descending through any 
arch, or chord of an arch, of a circle, as at C, in the 
lowest point C, is equal to the velocity that would be ac¬ 
quired in falling through the perpendicular height F C. 

Pendulums in motion have the same properties, the 
rod or string acting as the smooth, curved surface. 

For illustrations of these properties, see Kater and 
Gardners Mechanics, p. 79, or any general treatise on 
that subject. 


ARTICLE 12. 

ON TIIE MOTION OF PROJECTILES. 

A projectile is a body thrown, or projected, in any di¬ 
rection; such as a stone from the hand, water spouting 
from any vessel, a ball from a cannon, &c., fig. G. 



CTIAP. I.] MECHANICS. 35 

Every projectile is acted upon by two forces at the 
same time; namely, Impulse and Gravity. 

By impulse or the projectile force the body will pass 
over equal distances, A B, B C, &c., in equal times by 
1st general law of motion, Art. 7, and by gravity, it de¬ 
scends through the spaces A G, G H, &c., which are as 
the squares of the times, by 3d law of falling bodies, Art. 
9. Therefore, by these forces compounded, the body will 
describe the curve A Q, called a parabola; and this will 
be the case in all, except perpendicular directions; the 
curve will vary with the elevation, yet it will still be 
what is called a parabola. 

If the body be projected at an angle of 45 degrees ele¬ 
vation, it will be thrown to the greatest horizontal dis¬ 
tance possible; and if projected with double velocity, it 
will describe a quadruple range. 


ARTICLE 13. 

OF CIRCULAR MOTION AND CENTRAL FORCES. 

If a body A, fig. 7, be suspended by a string A C, and 
caused to move round the centre C, that tendency which 
it has to fly from the centre, is called the centrifugal 
force; and the action upon a body, which constantly so¬ 
licits it towards a centre, is called the centripetal force. 
This is represented by the string, which keeps the body 
A in the circle A M. Speaking of these two forces in¬ 
differently, they are called central forces* 

The particular laws of this species of motion are, 

1. Equal bodies, describing equal circles in equal times, 
have equal central forces. 

2. Unequal bodies, describing equal circles in unequal 
times, their central forces are as their quantities of mat¬ 
ter multiplied into their velocities. 


* It may be well to observe here, that this central force is no real power, 
but only an effect of the power that gives motion to the body. Its inertia 
causes it to recede from the centre, and fly off in a direct tangent, with the 
circle it moves in; therefore, this central force can neither add to, nor diminish, 
the power of any mechanical or hydraulic engine unless it be by friction and 
inertia, where water is the moving power, and the machine changes its direction. 



36 


MECHANICS. 


[CHAP. I. 

S. Equal bodies describing unequal circles in equal 
times, their velocities and central forces are as their 
distances from their centres of motion, or as the radii 
of their circles.* 

4. Unequal bodies describing unequal circles in equal 
times, their central forces are as their quantities of matter 
multiplied into their distances from their centres, or the 
radii of their circles. 

5. Equal bodies describing equal circles in unequal 
times, their central forces are as the square of their ve¬ 
locities; or, in other words, a double velocity generates 
a quadruple central force.f Therefore, 

6. Unequal bodies describing equal circles in unequal 
times, their central forces are as their quantities multi¬ 
plied into their velocities. 

7. Equal bodies describing unequal circles with equal 
celerities, their central forces are inversely as their dis¬ 
tances from their centres of motion, or the radii of their 
circles.J 

* This shows that when mill-stones are of unequal diameters, and revolve in 
equal times, the largest should have the draught of their furrows less, in pro¬ 
portion as their central force is more, which is in inverse proportion; also, 
that the draught of a stone should vary, and be in inverse proportion to the dis¬ 
tance from the centre. That is, the greater the distance the less the draught. 

Hence, we conclude, that if stones revolve in equal times, their draught 
must be equal near the centre; that is, so much of the large stones as is equal 
to the size of the small ones, must be of equal draught. But that part which 
is greater must have less draught in inverse proportion; as the distance from 
the centre is greater, the furrows must cross at so much less angle, which will 
be nearly the case (if their furrows lead to an equal distance from their centres) 
at any considerable distance from the centre of the stone; but near the centre 
the angles become greater than the proportion; if the furrows be straight, as 
appears by the lines, g 1, h 1, g 2, h 2, g 3, h 3, in fig. 1, PI. XI., the angles 
near the centre are too great, which seems to indicate that the furrows of mill¬ 
stones should not be straight, but a little curved; but what this curve should 
be, is very difficult to lay down exactly in practice. By theory it should be 
such as to cause the angle of furrows crossing, to change in inverse proportion 
with the distance from the centre, which will require the furrows to curve 
more as they approach the centre. 

f This shows that mill-stones of equal diameters, having their velocities un¬ 
equal, should have the draught of their furrows as the square roots of their 
number of revolutions per minute. Thus, suppose the revolutions of one stone, 
the furrows of which are correctly made, to be 81 per minute, and the mean 
draught of the furrows 5 inches, and found to be right, the revolutions of the 
other stone to be 100; then, to find the draught, say as the square root of 81, 
which is 9, is to the 5 inches draught, so is the square root of 100, which is 10, 
to 4.5 inches, the draught required (by inverse proportion,) because the draught 
must decrease as the central force increases. 

+ That is, the greater the distance, the less the central force. This shows that 
mill-stones of different diameters, having their peripheries revolving with equal 
velocities, should have the angle of draught, with which their furrows cros& 



MECHANICS. 


37 


CHAP. I.] 

8. Equal bodies describing unequal circles, having 
their central forces equal; their periodical times are as 
the square roots of their distances. 

9. Therefore the squares of the periodical times are 
proportional to the cubes of their distances, when neither 
the periodical times nor the celerities are given. In 
that case, 

10. The central forces are as the squares of the dis¬ 
tances inversely.* 


each other, in inverse proportion to their diameters, beause their central forces 
are as their diameters, by inverse proportion directly; and the angle of draught 
should increase, as the central force decreases, and decrease, as it increases. 

But here we must consider, that, to give stones of different diameters equal 
draughts, the distance of their furrows from the centre must be in direct pro¬ 
portion to their diameters. Thus, as 4 feet diameter is to 4 inches draught, so 
is 5 feet diameter to 5 inches draught. To make the furrows of each pair of 
stones cross each other at equal angles, in all proportional distances from the 
centre, see fig. 1, PI. XI., where g b, g d, g f, h a, h c, and h e, show the direc¬ 
tion of the furrows of the 4,5 and 6 feet stones, with their proportional draughts: 
now it is obvious that they cross each other at equal angles, because the re¬ 
spective lines are parallel, and cross in each stone near the middle of the radius; 
which shows that in all proportional distances, they cross at equal angles, con¬ 
sequently their draughts are equal. 

But the draught must be farther increased with the diameter of the stone, in 
order to increase the angle of draught in the inverse ratio, as the central force 
decreases. 

To do which, say,—If the 4 feet stone has central force equal 1, what central 
force will the 5 feet stone have ? Answer: 8, by the 7th law. 

Then say,—If the central force 1 require 5 inches draught, for a 5 feet stone, 
what will central force 8 require? Answer: 6.25 inches draught. This is sup¬ 
posing the verge of each stone to move with equal velocity. This rule may 
bring out the draught nearly true, provided there be not much difference be¬ 
tween the diameter of the stones. But it appears to me that neither the angle 
with which the furrows cross, nor the distance of the point from the centre, to 
which they direct, is a true measure of the draught. 

* These are the laws of circular motion and central forces. For experimental 
demonstrations of them, see Ferguson’s Lectures on Mechanics, page 27 to 47. 

I may here observe that the whole planetary system is governed by these 
laws of circular motion and central forces. Gravity acting as the string, is the 
centripetal force; and as the power of gravity decreases as the square of the dis¬ 
tance increases, and as the centripetal and centrifugal forces must always be 
equal, in order to keep the body in a circle; hence appears the reason why the 
planets most remote from the sun have their motion so slow, while those near 
him have their motions swift; because their celerities must be such as to create 
a centrifugal force equal to the attraction of gravity. 


38 


MECHANICS. 


[CHAP. 3. 


ARTICLE 14. 

OF TIIE CENTRES OF MAGNITUDE, MOTION AND GRAVITY. 

1. The centre of magnitude is that point which is 
equally distant from all the external parts of a body. 

2. The centre of motion is that point which remains 
at rest while all other parts of the body move round it. 

3. The centre of gravity of bodies is of great conse¬ 
quence to be well understood, it being the principle of 
much mechanical motion, it possesses the following par¬ 
ticular properties. 

1. If a body be suspended on this point as its centre 
of motion, it will remain at rest in any position. 

2. If a body be suspended on any other point than 
its centre of gravity, it can rest only in such position, 
that a right line drawn from the centre of the earth 
through the centre of gravity will intersect the point of 
suspension. 

3. When this point is supported, the whole body is 
kept from falling. 

4. When this point is at liberty to descend in a right 
line, the whole body will fall. 

5. The centre of gravity of all homogeneal bodies, as 
squares, circles, spheres, &c., is the middle point in a 
line connecting any two opposite points or angles. 

6. In a triangle, it is in a right line drawn from any 
angle to bisect the opposite side, and at the distance of 
one-third of its length from the side bisected. 

T. In a hollow cone, it is in a right line passing from 
the apex to the centre of the base, and at the distance 
of one-third of the side from the base. 

8. In a solid cone, it is one-fourth of the side from the 
base, in a line drawn from the apex to the centre of the 
base. 

The solution of many curious phenomena, as, why 
many bodies stand more firmly on their bases than others; 
and why some bodies lean considerably over without 
falling, depends upon a knowledge of the position of the 
centre of gravity. 

Hence appears the reason, why wheel-carriages, load- 




CHAP. II.] MECHANICS. 39 

ed with stones, iron, or any heavy matter, will not over¬ 
turn so easily, as when loaded with wood, hay, or any 
light article; for when the load is not higher than a b, 
fig, 22, a line from the centre of gravity will fall within 
the centre of the base at c; but if the load be as high as 
d, it will then fall outside the base of the wheels at e, 
consequently it will overturn. From this appears the 
error of those who hastily rise in a coach or boat when 
it is likely to overset, thereby throwing the centre of gra¬ 
vity more out of the base, and increasing their danger. 


CHAPTER II. 


ARTICLE 15 

OF THE MECHANICAL POWER. 

Having premised and considered all that is necessary 
for the better understanding those machines called me¬ 
chanical powers, we now proceed to treat of them. 
They are six in number; namely: 

The Lever, the Pulley, the Wheel and Axle, the In¬ 
clined Plane, and the Screw. 

These are called Mechanical Powers, because they in¬ 
crease our power of raising or moving heavy bodies. Al¬ 
though they are six in number, yet they are all governed 
by one simple principle, which I shall call the first Gene¬ 
ral Law of Mechanical Powers: it is this: the momentums 
of the poicer and weight are always equal , when the engine 
is in equilibrio. 

Momentum here means the product of the weight of 
the body multiplied into the distance it moves; that is, 
the power multiplied into its distance moved, or into its 
distance from the centre of motion, or into its velocity, 
is equal to the weight multiplied into its distance moved, 
or into its distance from the centre of motion, or into its 
velocity; or, the power multiplied into its perpendicular 
descent, is equal to the weight multiplied into its perpen¬ 
dicular ascent. 



40 


MECHANICS. 


[CHAP. II. 

The Second General Law of Mechanical Powers is, 

The power of the engine , and velocity of the weight moved 
are always in the inverse proportion to each other; that is, 
the greater the velocity of the weight moved, the less it 
must be; and the less the velocity the greater the weight 
may be; and that universally in all cases. 

The Third General Law is, 

Part of the original power is ahoays lost in overcoming 
friction , inertia , <f*c., hut no power can he gained hy engines , 
when time is considered in the calculation . 


In the theory of this science, we suppose all planes to 
be perfectly smooth and even, levers to have no weight, 
cords to be perfectly pliable, and machines to have no 
friction; in short, all imperfections are to be laid aside, 
until the theory is established, and then proper allow¬ 
ances are to be made for them. 


ARTICLE 16. 

OF THE LEVER. 

A bar of iron, of wood, or of any other inflexible ma¬ 
terial, one part of which is supported by a fulcrum or 
prop, and all other parts turn or move on that prop, as 
their centre of motion, is called a lever: when the lever 
is extended on each side of the prop, these extensions 
are called its arms: the velocity or motion of every part 
of these arms is directly as its distance from the centre 
of motion, by the third law of circular motion. 

With respect to the lever, when in equilibrium, 
observe the following laws:— 

1. The power and weight are to each other, inverse¬ 
ly as their distances from the prop, or centre of mo¬ 
tion. 

That is, the power P, fig. 8, Plate I, which is one 
multiplied into its distance B C, from the centre 12, is 
equal to the weight 12 multiplied into its distance A B 
1; each product being 12. 







MECHANICS. 


41 


CHAP. II.] 

2. The power is to the weight, as the distance the 
weight moves is to the distance the power moves, re¬ 
spectively. 

That is, the power multiplied into its distance moved, 
is equal to the weight multiplied into its distance moved. 

3. The power is to the weight, as the perpendicular 
ascent of the weight is to the perpendicular descent of 
the power. 

That is, the power multiplied into its perpendicular 
descent, is equal to the weight multiplied into its perpen¬ 
dicular ascent. 

4. Their velocities are as their distances from their 
centre of motion, by the 3d law of circular motion, p. 28. 

These simple laws hold universally true, in all me¬ 
chanical powers or engines; therefore, it is easy (from 
these simple principles) to compute the power of any 
engine, either simple or compound; for it is only to find 
how much swifter the power moves than the weight, or 
how much farther it moves in the same time; and so 
much is the power (and time of producing it) increased, 
by the help of the engine. 


ARTICLE 17. 


GENERAL RULES FOR COMPUTING THE POWER OF ANY ENGINE. 

1. Divide either the distance of the power from its 
centre of motion, by the distance of the weight from its 
centre of motion. Or, 

2. Divide the space passed through by the power, by 
the space passed through by the weight, (this space may 
be counted either on the arch, or on the perpendicular 
described by each,) and the quotient will show how 
much the power is increased by the help of the engine; 
then multiply the power applied to the engine, by that 
quotient, and the product will be the power of the engine, 
whether simple or compound. 



42 


MECHANICS. 


[CHAP. II. 


EXAMPLES. 

Let ABC, Plate I. fig. 8, represent a lever; then, to 
compute its power, divide the distance of the power P 
from its centre of motion B C 12, by the distance A B 1, 
of the weight W, and the quotient is 12: the power is 
increased 12 times by the engine; which, multiplied by 
the power applied 1, produces 12, the power of the en¬ 
gine at A, or the weight W, that will balance P, and 
hold the engine in equilibrio. But suppose the arm A 
B to be continued to E, then, to find the power of the 
engine, divide the distance B C 12, by B E 6, and the 
quotient is two; which, multiplied by 1, the power ap¬ 
plied, produces 2, the power of the engine, or weight IV, 
to balance P. 

Or divide the perpendicular descent C D of the power 
equal to 6, by the perpendicular ascent E F, equal 3; 
and the quotient 2, multiplied by the power P, equal 1, 
produces 2, the power of the engine at E. 

Or divide the velocity of the power P, equal 6, by the 
velocity of the weight w, equal 3; and the quotient 2 
multiplied by the power 1, produces 2, the power of the 
engine at E. If the power P had been applied at 8, then 
it would have required to have been to balance W, 
or w: because 1~ times 8 is 12, which is the momentum 
of both weights W and w. If it had been applied at 6, 
it must have been 2; if at 4, it must have been 3; and 
so on for any other distance from the prop or centre of 
motion. 


ARTICLE 18. 

OF THE DIFFERENT KINDS OF LEVERS. 

There are four hinds of Levers. 

1. The most common kind, where the prop is placed 
between the weight and power, but generally nearest the 
weight, as otherwise there would be no gain of power. 

2. When the prop is at one end, the power at the 
other, and the weight between them. 










CHAP. II.] MECHANICS. 43 

3. When the prop is at one end, the weight at the 
other, and the power applied between them. 

4. The bended lever, which differs only in form, but 
not in properties, from the others. 

Those of the first and second kind have the same pro¬ 
perties and powers, and produce real mechanical advan¬ 
tage, because they increase the power; but the third kind 
produces a decrease of power, and is only used to increase 
velocity, as in clocks, watches, and mills, where the first 
mover is slow, and the velocity is increased by the gear¬ 
ing of the wheels. 

The levers which nature employs in the machinery of 
the human frame are of the third kind; for when we lift 
a weight by the hand, the muscle that exerts the force 
to raise the weight, is fastened at about one-tenth of the 
distance from the elbow to the hand, and must exert a 
force ten times as great as the weight raised; therefore, 
he that can lift 56 lbs. with his arm at a right angle at 
the elbow, exerts a force equal to 560 lbs. by the muscles 
of his arm. 


ARTICLE 19. 

OF COMPOUND LEVERS. 

Several levers may be applied to act one upon another, 
as 2 1 3 in fig. 9, Plate I, where No. 1 is of the first 
kind, No. 2 of the second, and No. 3 of the third. The 
power of these levers, united to act on the weight W, is 
found by the following rule, which will hold universally 
true in any number of levers united, or wheels (which 
operate on the same principle) acting upon one another. 

RULE. 

1st. Multiply the power P, into the length of all the 
driving levers successively, and note the product. 

2d. Then multiply all the leading levers into one ano¬ 
ther successively, and note the product. 



44 


MECHANICS. 


[CHAP. II. 

3d. Divide the first product by the last, and the quo- 
tient will be the weight W, that will hold the machine in 
equilibrio. 

This rule is founded on the first law of the lever, Art. 
16, and on this principle; namely: 

Let the weight W, and power P, be such, that when 
suspended on any compound machine, whether of levers 
united, or of wheels and axles, they hold the machine in 
equilibrio: then if the power P be multiplied into the 
radius of all the driving wheels, or lengths of the driving 
levers, and the product noted, and the weight W multi¬ 
plied in the radius of all the leading wheels, or lengths of 
the leading levers, and the product noted, these products 
will be equal. If we had taken the velocities, or the cir¬ 
cumferences of the wheels, instead of their radii, they 
would have been equal also. 

On this principle is founded all rules for calculating 
the power and motion of wheels in mills, &c. See Art. 
20 . 

EXAMPLES. 

Given the power P equal to 4 on lever 2, at 8 distance 
from the centre of motion. Required, with what force 
lever 1, fastened at 2 from the centre of motion of lever 
2, must act to hold the lever 2 in equilibrio. * 

By the rule, 4x8 the length of the long arm is 32, and 
this divided by 2, the length of the short arm, gives 16, 
the force required. 

Then 16 on the long arm, lever 1, at 6 from the centre 
of motion. Required the weight on the short arm, at 2, 
to balance it. 

By the rule, 16x6 = 96, which divided by 2, the short 
arm, gives 48, for the weight required. 

Then 48 is on the lever 3, at 2 from the centre. Re¬ 
quired the weight at 8 to balance it. 

Then 48 x 2 = 96, which divided by 8, the length of 
ong arm, gives 12, the weight required. 

Given the power P = 4, on one end of the combination 


* In order to abbreviate the work, I shall hereafter use the following Alge¬ 
braic signs, namely: 




MECHANICS. 


CHAP. II.] 



of levers. Required, the weight W. on the other end, 
to hold the whole in equilibrio. 

Then by the rule, 4x8x6x2= 384 the product of 
the power multiplied into the length of all the driving 
levers, and 2 x 2 x 8 = 32 the product of all the leading 
levers, and 384 — 32 = 12 the weight W required. 


ARTICLE 20. 

CALCULATING THE POWER OF WHEEL WORK. 

The same rule holds good in calculating the power oi 
machines consisting of wheels, whether simple or com¬ 
pound, by counting the radii of the wheels as the levers; 
and because the diameters and circumferences of circles 
are proportional, we may take the circumferences instead 
of the radii, and it will be the same result. Then, again, 
because the number of cogs in the wheels constitute the 
circle, we may take the number of cogs and rounds in¬ 
stead of the circle or radii, and the result will still be 
the same. 

Let fig. 11, Plate II, represent a water mill (for grind¬ 
ing grain) double-geared. 

Number 8, The water-wheel, 

4, The great cog-wheel, 

2, The wallower, 

3, The counter cog-wheel, 

1, The trundle, 

2, The mill-stones, 

And let the above numbers also represent the radius 
of each wheel in feet. 

Now suppose there be a power of 500 lbs. on the water¬ 
wheel required, what will be the force exerted on the 
mill-stone, 2 feet from the centre. 


The sign -f- plus, or more, for addition. 

— minus, or less, for subtraction. 

X multiplied, for multiplication. 

-f- divided, for division. 

= equal, for equality. 

Then, instead of 8 more 4 equal 12, I shall write 8 -f 4 = 12. Instead of 12 
less 4 equal 8,12 — 4=8. Instead of 6 multiplied by 4 equal 24, G x 4 = 24. 
And instead of 24 divided by 3 equal 8, 24 3 = 8. 



4G 


MECHANICS. 


[chap. n. 

Then by the rule, 500 x 8 x 2 x 1 = 8000, and 4x3 
x 2 = 24, by which divide 8000, and it quotes 333,33 lbs. 
the power or force required, exerted on the mill-stone 
two feet from its centre, which is the mean circle of a 6 
feet stone.—And as the velocities are as the distance 
from the centre of motion, by the third law of circular 
motion, Art. 13, therefore, to find the velocity of the 
mean circle of the stone 2, apply the following rule; 
namely: 

1st. Multiply the velocity of the water-wheel into the 
radii or circumferences of all the driving wheels, succes¬ 
sively, and note the product. 

2d. Multiply the radii or circumferences of all the 
leading wheels, successively, and note the product; di¬ 
vide the first by the last product, and the quotient will 
be the answer. 

But observe here, that the driving wheels in this 
rule, are the leading levers on the last rule. 

EXAMPLES. 

Suppose the velocity of the water-wheel to be 12 feet 
per second; then by the rule 12 x4x3x2 = 288 and 
8x2x1 = 16, by which divide the first product 288, 
and this gives 18 feet per second, the velocity of the 
stone 2 feet from its centre. 


ARTICLE 21. 

TOWER DECREASES AS MOTION INCREASES. 

It may be proper to observe here, that as the velocity 
of the stone is increased, the power to move it is de¬ 
creased, and as its velocity is decreased, the power on 
it to move it is increased, by the second general law of 
mechanical powers. This holds universally true in all 
engines that can possibly be contrived; which is evident 
from the first law of the lever when in equilibrium, 
namely, the power multiplied into its velocity or dis¬ 
tance moved, is equal to the weight multiplied into its 
velocity or distance moved. 










MECHANICS. 


47 


CHAP. II.] 

Hence the general rule to compute the power of any 
engine, simple or compound, Art. 17. If you have the 
moving power, and its velocity or distance moved, given, 
and the velocity or distance of the weight, then, to find 
the weight, (which, in mills, is the force to move the 
stone, &c.) divide that product by the velocity of the 
weight or mill-stone, &c., and this gives the weight or 
force exerted on the stone to move it. But a certain 
quantity or proportion of this force is lost from friction 
in order to obtain a velocity to the stone; which is 
shown in Art. 31. 


ARTICLE 22. 

NO POWER GAINED BY ENLARGING OVERSHOT WATER-WHEELS. 

This seems a proper time to show the absurdity of the 
idea of increasing the power of tlie mill, by enlarging the 
diameter of the water-wheel, on the principle of length¬ 
ening the lever; or by double gearing mills where sin¬ 
gle gears will do; because the power can either be in¬ 
creased or diminished by the help of engines, while the 
velocity of the body moved is to remain the same. 

EXAMPLE. 

Suppose we enlarge the diameter of the water-wheel 
from 8 to 16 feet radius, fig. 11, Plate II. and leave the 
other wheels unaltered; then, to find the velocity of 
the stone, allowing the velocity of the periphery of the 
water-wheel to be the same (12 feet per second;) by 
the rule 12 x4x3x2 = 288, and 16 x 2 x 1 = 32, 
by which divide 288, which gives 9 feet in a second, 
for the velocity of the stone. 

Then, to find the power by the' rule for that purpose, 
Art. 20, 500 x 16 x 2 x 1 = 16,000, and 4x3x2 = 
24, by which divide 16,000, it gives 666,66 lbs. the 
power. But as velocity as well as power is necessary in 



48 


MECHANICS. 


[CHAP. II. 

mills, we shall be obliged, in order to restore the velo¬ 
city, to enlarge the great cog-wheel from 4 to 8 radius. 

Then to find the velocity, 12 x 8 x 3 x 2 = 576, 
and 16 x 2 x 1 = 32, by which divide 576, it gives 
18, the velocity as before. 

Then to find the power by the rule, Art. 20, it will 
be 333,33 as before. 

Therefore no power can be gained, upon the princi¬ 
ple of lengthening the lever, by enlarging the water¬ 
wheel. 

The true advantages that large wheels have over small 
ones, arise from the width of the buckets bearing but a 
small proportion to the radius of the wheel; because if 
the radius of the wheel be 8 feet, and the width of the 
bucket or float board but 1 foot, the float takes up 1-8 of 
the arm, and the water may be said to act fairly upon 
the end of the arm, and to advantage. But if the radius 

of the wheel be but 2 feet, and the width of the float 1 

/ 

foot, part of the water will act on the middle of the arm, 
and of course, to disadvantage, as the float takes up half 
the arm. The large wheel also serves the purpose of a 
fly-wheel (Art. 30;) it likewise keeps a more regular 
motion, and casts off back water better. (See Art. 70.) 

But the expense of these large wheels is to be taken 
into consideration, and then the builder will find that 
there is a maximum size, (see Art. 44,) or a size that 
will yield him the greatest profit. 


ARTICLE 28. 

NO POWER GAINED, BUT SOME LOST, BY DOUBLE GEARING MILLS. 

I might go on to show that no power or advantage is 
to be gained by double gearing mills, upon any other 
principles than the following; namely: 

1. When the motion'necessary for the stone cannot be 
obtained without having the trundle too small, we are 
obliged to have the pitch of the cogs and rounds, and the 
size of the spindle, large enough to bear the stress of the 






MECHANICS. 


49 


CHAP. II.] 

power; and this pitch of gear, and size of spindle, may . 
bear too great a proportion to the radius of the trundle, 
(as does the size of the float to the radius of the water¬ 
wheel, Art. 22,) and may work hard. There therefore 
may be a loss of power on that account, greater than that 
resulting from friction in double gearing. 

2. By double gearing, the mill may be made more con¬ 
venient for two pairs of stones to one water-wheel. 

Many and great have been the losses sustained by mill 
builders on account of their not properly understanding 
these principles. I have often met with water wheels 
of large diameter, where those of half the size and ex¬ 
pense would answer better; and double gears, where 
single would be preferable. 


ARTICLE 24. 

OF THE PULLEY. 

2. The pulley is a mechanical power well known. 
One pulley, if it be movable with the weight, doubles 
the power, laecause each rope sustains half the weight. 

If two or more pulleys be joined together in the com¬ 
mon way, then the easiest mode of computing their power 
is, to count the number of ropes that join to the lower or 
movable block, and so many times is the power increased; 
because all these ropes have to be shortened, and all run 
into one rope (called the fall) to which the moving power 
is applied. If there be 4 ropes, the power is increased 
fourfold. See Plate I. fig 10. 

The objection to this engine is, that there is great loss 
of power, by the friction of the pulleys, and in the bend¬ 
ing of the ropes. 


ARTICLE 25. 

OF THE WHEEL AND AXLE. 

3. The wheel and axle, fig. 17, is a mechanical power, 
similar to the lever of the first kind; therefore, when 
4 




50 


MECHANICS. 


[CHAP. II. 

the power is to the weight as the diameter of the axle is 
to the diameter of the wheel; or when the power multi¬ 
plied into the radius of the wheel is equal to the weight 
multiplied into the radius of the axle, this engine is in 
equilibrium. 

The loss of power is but small in this instrument, be¬ 
cause it has but little friction. 


ARTICLE 26. 

OF THE INCLINED PLANE. 

4. The inclined plane is the fourth mechanical power; 
and in this the power is to the weight, as the perpendicu¬ 
lar height of the plane is to its length. This is of use in 
rolling heavy bodies, such as barrels, hogshead, &c., into 
wheel carriages, &c., and for letting them down again. 
See Plate I. fig. 5. If the height of the plane be half its 
length, then half the force will roll the body up the plane, 
that would lift it perpendicularly to the same height, 
but it lias to travel double the distance. 


ARTICLE 27. 

OF THE WEDGE. 

5. The wedge is only an inclined plane. Whence, in 
the common form of it, the power applied will be to the 
resistance to be overcome, as the thickness of the wedge 
is to the length thereof. This is a very useful mechani¬ 
cal power, and, for some purposes, excels all the rest; 
because with it we can effect what we cannot with any 
other in the same time; and its power, I think, may be 
computed in the following manner. 

If the wedge be 12 inches long and 2 inches thick, 
then the power to hold it in equilibrio is as 1 to balance 
12 resistance; that is 12 resistance pressing on each side 
of the wedge; and when struck with a mallet the whole 
force of the weight of the mallet, added to the whole 




CHAP. II.] MECHANICS. 51 

force of the power exerted in the stroke, is communi¬ 
cated to the wedge in the time it continues to move: and 
this force, to produce effect, is as the square of the veloci¬ 
ty with which the mallet strikes, multiplied into its 
weight; therefore, the mallet should not be too large, 
because it may be too heavy for the workman’s strength, 
and will meet too much resistance from the air, so that 
it will lose more by lessening the velocity than it will 
gain by its weight. Suppose a mallet of 10 lbs. strike 
with 5 velocity, its effective momentum is 250; but if 
it strike with 10 velocity, then its effective momentum 
is 1000. The effect produced by the strokes will be as 
250 to 1000; and all the force of each stroke, except 
what may be destroyed by the friction of the wedge, is 
added in the wedge, until the sum of these forces 
amounts to more than the resistance of the body to be 
split, which, therefore, must give way; but when the 
wedge does not move, the whole force is destroyed by 
the friction; therefore, the less the inclination of the 
sides of the wedge, the greater the resistance we can 
overcome by it, because it will be easier moved by the 
stroke. 


ARTICLE 28. 

OF THE SCREW. 

G. The screw is the last-mentioned mechanical power, 
and may be denominated a circular inclined plane, (as 
will appear by wrapping a paper, cut in form of an in¬ 
clined plane, round a cylinder.) It is used in combina¬ 
tion with a lever of the first kind, (the lever being ap¬ 
plied to force the weight upon the inclined plane:) this 
compound instrument is a mechanical power, of exten¬ 
sive use, both for pressure and raising great weights. 
The power applied is to the weight it will raise, as the 
distance through which the weight moves, is to the dis¬ 
tance through which the power moves; that is, as the dis¬ 
tance of two contiguous threads of the screw is to the cir¬ 
cle the power describes, so is the power to the weight it 
will raise. If the distance of the thread be half an inch, 



MECHANICS. 



[CHAP. II. 


and the lever be fifteen inches radius, and the power ap¬ 
plied be 10 lbs., then the power will describe a circle of 
94 inches, while the weight rises half an inch; then as 
half an inch is to 94 inches, so is 10 lbs. to 1880 lbs., the 
weight the engine would raise with 10 lbs. power. But 
this is supposing the screw to have no friction, of which 
it has a great deal. 


ARTICLE 29. 

v 

or THE FLY-WHEEL, AND ITS USE. 

Before I dismiss the subject of mechanical powers, I 
shall take some notice of the fly-wlieel, the use of which 
is to regulate the motion of engines, it is best made of 
cast iron, and should be of a circular form, that it may 
not meet with much resistance from the air. 

Many have supposed this wheel to be an increaser of 
power, whereas it is, in reality, a considerable destroyer 
of it; which appears evident, when we consider that it 
has no motion of its own, but receives all its motion * 
from the first mover, and as the friction of the gudgeons, 
and the resistance of the air are to be overcome, this 
cannot be done without the loss of some power; yet 
this wheel is of great use in many cases; namely: 

1st. For regulating the power where it is irregularly 
applied; such as the treadle and crank moved by the 
foot or hand; as in spinning-wheels, turning-lathes, flax- 
mills, or where steam is applied by a crank to produce 
a circular motion. 

2d. Where the resistance is irregular, or by jerks, as 
in saw-mills, forges, slitting-mills, powder-mills, &c., the 
fly-wheel by its inertia, regulates the motion; because 
if it be very heavy, it will require a great many little 
shocks or impulses of power to give it a considerable 
velocity; and it will, of course, require as many equal 
shocks to resist or destroy the velocity it has acquired. 

While a rolling or slitting-mill is running empty, the 





MECHANICS. 


53 


CHAP. II.] 

force of the water is employed in generating momentum 
in the fly-wheel; which force accumulated in the fly, will 
be sufficient to continue the motion without much abate¬ 
ment, while the sheet of metal is running between the 
rollers; whereas, had the force of the water been lost 
while the mill was empty, its motion might be destroyed 
before the metal passed through the rollers.-' Where 
water is scarce, its effect may be so far aided by a fly¬ 
wheel, as to overcome a resistance to which the direct 
force of the water is unequal, that is, where the power 
is required at intervals only. 

A heavy water-wheel frequently produces all the ef¬ 
fect of a fly-wheel, in addition to its direct office. 


ARTICLE 30. 

ON FRICTION. 

We have hitherto considered the action and effect of 
the mechanical powers, as they would answer to the 
strictness of mathematical theory, were there no such 
thing as friction, or rubbing of parts upon each other; 
but it is generally allowed that one-fourth of the effect 
of a machine is, at a medium, destroyed by it: it will 
be proper to treat of it next in course. 

From what I can gather from different authors, and 
by my own experiments, it appears that the doctrine of 
friction is as follows, and we may say it is subject to 
the following laws, namely: 

Laics of Friction. 

1. Friction is greatly influenced by the smoothness or 
roughness, hardness or softness of the surface rubbing 
against each other. 

2. It is in proportion to the pressure or load, that is, a 
double pressure will produce a double amount of fric¬ 
tion ; a triple pressure a triple amount of friction, and 
so of any other proportionate increase of the load. 

3. The friction does not depend upon the extent of 
surface, the weight of the body remaining the same. 



54 


MECHANICS. 


[CHAP. II. 

Thus, if a parellelopiped, say of four inches in width and 
one in thickness, as F, plate II. fig. 13, be made smooth, 
and laid upon a smooth plane A. B. C. D. and the weight 
P. hung over a pulley, it will require the weight P. to 
draw the body F. along, to be equal, whether it be laid 
on its side or on its edge. 

The experiments of Vince led him to conclude that 
the law, as thus laid down, was not correct; but those 
more recently performed justify the conclusion that it 
is so; the deviations being so trifling as not to affect the 
general result. 

4. The friction is greater after the bodies have been 
allowed to remain for some time at rest, in contact with 
each other, than when they are first so placed; as, for 
example, a wheel turning upon gudgeons will require a 
greater weight to start it after remaining for some 
hours at rest, than it would at first. 

The cause of this appears to be that the minute aspe¬ 
rities which exist even upon the smoothest bodies, gra¬ 
dually sink into the opposite spaces, and thus hold upon 
each other. 

It is for the same reason that a greater force is re¬ 
quired to set a body in motion than to keep it in motion. 
If about one-third the amount of a weight be required to 
move that weight along in the first instance, one-fourtli 
will suffice to keep it in motion. 

5. The friction of axles does not at all depend upon 
their velocity: thus a rail-road car travelling at the rate 
of twenty miles an hour, will not have been retarded by 
friction more than another which travels only ten miles - 
in that time. 

It appears therefore, from the last three laws, that the 
amount of friction is as the pressure directly, without 
regard to surface, time or velocity. 

6. Friction is greatly diminished by unguents, and this 
diminution is as the nature of the unguents, without re¬ 
ference to the substances moving over them. The kind 
of unguent which ought to be employed, depends prin¬ 
cipally upon the load; it ought to suffice just to prevent 
the bodies from coming into contact with each other. 
The lighter the weight, therefore, the finer and more 
fluid should be the unguent, and vice versa. 









CHAP. II.] 


MECHANICS. 


55 


ARTICLE 31. 

* 

ON THE FRICTION OF DIFFERENT SUBSTANCES. 

It is well known that in general the friction of two 
dissimilar substances is less than that of similar sub¬ 
stances, although alike in hardness. The most recent 
experiments upon this subject are those of Mr. Rennie, of 
England, performed in the year 1825, and published in 
the Philosophical Transactions. Many of the experi¬ 
ments were performed upon substances which do not 
concern the present work; those with the metals, and 
other hard substances, were tried both with and with¬ 
out unguents. 

The following facts were deduced from those in which 
unguents were not employed: 

Table showing the amount of friction (without unguents ) of different 
substances , the insistent weight being 36 lbs., and within the limits of 
abrasion of the softer substances. 


Parts of the 
whole weights. 

Brass on wrought iron, - - - 7.38 

Brass on cast iron, - - - - - 7.11 

Brass on steel, ----- 7.20 

Soft steel on soft steel, - - - - 6.85 

Cast iron on steel, - - - - - 6.62 

Wrought iron on wrought iron, - - - 6.26 

Cast iron on cast iron, - - - - 6.12 

Hard brass on cast iron, - - - 6.00 

Cast iron on wrought iron, - - - - 5.87 

Brass on brass, - - - - - 5.70 

Tin on cast iron, - - - - - 5.59 

Tin on wrought iron, - 5.53 

Soft steel on wrought iron, - - - - 5.28 


With unguents it was found that with gun metal on 
cast iron, with oil intervening, the insistent weight be¬ 
ing 10 cwt., the friction amounted to of the pressure; 
that by a diminution of weight the friction was rapidly 
diminished. 

That cast iron on cast iron, under similar circum¬ 
stances, showed less friction; and that this was still far¬ 
ther diminished by hog’s lard. 


I 


56 MECHANICS. [C*IAP. II. 

That yellow brass on cast iron, with anti-attrition 
composition of black lead and hog’s lard, increased fric- 
tion with light weights, and greatly diminished it with 
heavy weights, showing extremely irregular results. 

That yellow brass on cast iron, with tallow, gave the 
least friction, and may therefore be considered the best 
substance under the circumstances tried. 

That yellow brass on cast iron, with soft soap, gave 
the second best result, being superior to oil. 


ARTICLE 32. 

OF MECHANICAL CONTRIVANCES TO REDUCE FRICTION. 

Friction is considered as of two kinds; the first is oc¬ 
casioned by the rubbing of the surfaces of bodies against 
each other, the second by the rolling of a circular body, 
as that of a carriage wheel upon the ground, or rollers 
placed under a heavy load. In the preceding articles 
the first kind of friction lias been considered; it is that 
which we most frequently have to encounter, and which 
produces the greatest expenditure of power. When the 
parts can be made to roll over each other, the resistance 
is greatly diminished. To change one into the other 
has been the object of those mechanical contrivances 
denominated friction wheels, and friction rollers. 

A, in plate II. fig. 14, may represent the gudgeon of 
a wheel set to run upon the peripheries of two wheels,- 
G, C, which pass each other; these are called friction 
wheels. This gudgeon, instead of grinding or rubbing 
its surface, or the surface on which it presses, carries that 
surface with it, causing the wheels C, C, to revolve. A 
gudgeon, B, is sometimes set upon a single wheel, with 
supporters to keep it on, which produces an analogous 
effect. 

Less advantage, however, has been derived from fric¬ 
tion wheels in heavy machinery, than had been antici¬ 
pated ; and it has been found, in many cases, that they do 
not compensate for the expense of construction, and their 









MECHANICS. 


57 


CHAP. II.] 

liability to get out of order. Tlie rubbing friction still 
exists in their gudgeons, and it has frequently happened 
that instead of turning them, the gudgeon resting upon 
them has rolled round, whilst they have remained at 
rest. 

The principle of the roller lias already been noticed, 
and its mode of action is shown in fig. 15, plate II., where 
A B may represent a body of a 100 tons weight, with the 
under side perfectly smooth and even, set on rollers per¬ 
fectly hard and smooth, rolling on a horizontal plane, C D, 
perfectly hard, smooth, and horizontal. If these rollers 
stand precisely parallel to each other, the least imagina¬ 
ble force would move the load; even a spider’s web would 
be sufficient, were time allowed to overcome the inertia. 

These suppositions, however, can never be realized, 
and although in this mode of action there will be the 
least possible rubbing friction, there will be enough to 
produce considerable resistance. 

It has been attempted to apply this principle to wheel 
carriages, to the sheaves of blocks on ship board, and to 
the axles of other machinery, by an ingenious contri¬ 
vance called Garnett’s friction rollers, for which a pa¬ 
tent was obtained in England, about fifty years ago, by 
an American gentleman from New Jersey. This con¬ 
trivance is shown at fig. 16, Plate II. The outside ring 
B, C, D, may represent the box of a carriage wheel, the 
inside circle A the axle; the circles a a a a a a the rol¬ 
lers round the axle, and between it and the box; the in¬ 
ner ring is a thin plate for the pivots of the rollers to run 
in, to keep them at a proper distance from each other. 
When the wheel turns, the rollers pass round on the 
axle, and on the inside of the box, and that almost with¬ 
out friction, because there is no rubbing of the parts in 
passing one another. 

Such friction rollers, from the use of which so much 
was expected, have not been found to answer in practice. 
If not made with the most perfect accuracy, they gather 
as they roll, and thus increase the friction. In carriages, 
and indeed in every kind of machines, subject to an ir¬ 
regular jolting motion, the rollers, and the cylinder with- 


MECHANICS. 


58 


[chap. II. 


in which they revolve, soon become indented, and are 
then w r orse than useless. 


ARTICLE 33. 

OF MAXIMUMS, OR THE GREATEST EFFECTS OF ANY MACHINE. 

The effect of a machine is the distance to which it 
moves a body of given weight, in a given time; or, in 
other words, the resistance which it overcomes. The 
weight of the body multiplied into its velocity, is the 
measure of this effect. 

The theory published by philosophers, and received 
and taught as true, for several centuries past, is, that 
any machine will work with its greatest perfection when 
it is charged with just 4-9ths of the power that v r ould 
hold it in equilibrio, and then its velocity will be just J 
of the greatest velocity of the moving power. 

To explain this, we may suppose the water-wheel 
Plate II. tig. 17, to be of the undershot kind, 16 feet di¬ 
ameter, turned by-water issuing from under a 4 feet head, 
with a gate drawn 1 foot wide, and 1 foot high, then the 
force will be 250 lbs., because that is the weight of the 
column of water above the gate, and its velocity will be 
16.2 feet per second, as shall be shown under the head 
of Hydraulics; the wheel will then be moved by a power 
of 250 lbs., and if let run empty, will move with a ve¬ 
locity of 16 feet per second; but if the weight W be hung 
by a rope to the axle of tw r o feet diameter, and we con¬ 
tinue to add to it until it stops the wheel, and holds it 
in equilibrio, the weight will be found to be 2000 lbs. by 
the rule, Art. 19; and then the effect of the machine is 
nothing, because the velocity is nothing: but as v^e de¬ 
crease the weight W, the vdieel begins to move, and its 
velocity increases accordingly; and then the product of 
the weight multiplied into its velocity, will increase 
until the weight is decreased to 4-9ths of 2000 = 888.7, 
which multiplied into its velocity or distance moved, 
will produce the greatest effect, and the velocity of the 





CHAP. II.] MECHANICS. 59 

wheel will then be | of 16 feet, or 5.33 feet per second. 
So say those who have treated of it. 

This will probably appear plainer to a beginner, if he 
conceives this wheel to be applied to work an elevator, 
as E, Plate II. fig. 17, to hoist wheat, and suppose that 
the buckets, when all full, contain nine pecks, and will 
hold the wheel in equilibrio, it is evident that it will 
then hoist none, because it has no motion; and in order 
to obtain motion, we must lessen the quantity in the 
buckets, when the wheel will begin to move, and hoist 
faster and faster until the quantity is decreased to 4- 
9ths or 4 pecks, and then, by the theory, the velocity of 
the machine will be A of the greatest velocity, when it 
will hoist the greatest quantity possible in a given time; 
for if we lessen the quantity in the buckets below 4 pecks, 
the quantity hoisted in any given time will be lessened: 
this is the established theory. ^ 


ARTICLE 34. 

OLD THEORY INVESTIGATED. 

In order to investigate this theory, and the better to 
understand what has been said, let us consider as follows; 
namely: 

1. That the velocity of spouting water, under 4 feet 
head, is 16 per second, nearly. 

2. The section or area of the gate drawn, in feet, 
multiplied by the height of the head in feet, gives the 
cubic feet in the whole column, which multiplied by 
62.5 (the weight of a cubic foot of water) gives the 
weight or force of the whole column pressing on the 
wheel. 

3. That the radius of the wheel, multiplied by the 
force, and that product divided by the radius, of the 
axle, gives the weight that will hold the wheel in equi¬ 
librio. 

4. That the absolute velocity of the wheel, subtracted 
from the absolute velocity of the water, leaves the re- 



MECHANICS. 


GO 


[chap. II. 


lative velocity with which the water strikes the wheel 
when in motion. 

5. That as the radius of the wheel is to the radius 
of the axle, so is the velocity of the wheel to the ve¬ 
locity of the weight hoisted on the axle. 

6. That the effects of spouting fluids, are as the 
squares of their velocities (see Art. 45, law G,) but the 
instant force of striking fluids is as their velocities 
simply. See Art. 8. 

7. That the weight hoisted, multiplied into its per¬ 
pendicular ascent gives the effect. 

8. That the weight of water expended, multiplied 
into its perpendicular descent, gives the power used per 
second. 

On these principles I have calculated the following 
scale: first, sivpposing the force of striking fluids to be 
as the square of their striking or relative velocity, which 
brings out the maximum agreeably to the old theory, 
namely: 

When the load at equilibrio is 2000, then the maxi¬ 
mum load is 888.7 = 4-9ths of 2000, the effect being 
then greatest, namely, 591.98, as appears in the sixth 
column; and then the velocity of the wheel is 5.333 feet 
per second, equal to -i of 16, the velocity of the water, 
as appears in the fifth line of the scale: but there is an 
evident error in the first principle of this theory, by 
counting the instant force of the water on the wheel to 
be as the square of its striking velocity; it cannot, there¬ 
fore, be true. See Art. 41. 

I then calculate upon this principle, namely: that if 
the instant force of striking fluids is as their velocity 
simply, then the load that the machine will carry, with 
its different velocities, will also be as the velocity simply, 
as appears in the 7th column; and the load, at a maxi¬ 
mum, as 1000 lbs. = \ of 2000, the load, at an equilibrio, 
when the velocity of the wheel is 8 feet = l of 16, the 
velocity of the water per second; and then the effect is 
at its greatest, as shown in the 8th column, namely, 
1000, as appears in the fourth line of the scale. 

This I call the new theory, (because I found that 




MECHANICS. 


61 


CHAP. II.] 

William Waring had also, about the same time, esta¬ 
blished it, see Art. 37,) namely, that when any ma¬ 
chine is charged with just one-lialf of the load that will 
hold it in equilibrio, its velocity will be just one-half of 
the natural velocity of the moving power, and then its 
effect will be at a maximum, or the greatest possible. 

It thus appears that a great error has been long over¬ 
looked by philosophers, and that this has rendered the 
theory of no use in practice, but led many into expen¬ 
sive failures. 




A scale for determining the Maximum Charge and Velocity of Undershot Mills. 


MECHANICS 


[CHAP. II 


Ratio of the power and effect 
at a maximum; the power 
being 4,000 in each case, - 


Maximum 

by new 

theory. 

4 to l 

10 to 1-47 

Maximum 

by old 

theory. 

Effect by the new theory, - 

1 feet. 

Ot-OMIOOOIO 

onooMciot- 

>ao©oooo>n 

Weight hoisted, according to 
the new theory, 

lbs. 

©0000)10 000 
o o o *o co r— o to o 
101>00)COCO*01>0 

1—1 1—1 r —1 1—1 T—1 r—1 O) 

Effect by the old theory, 

feet. 

00 

to oo^ion 

I-* <— 1 O to 1-1 O O) O) 

OOOIOOOOOOOX) 
h .15 o ui o n 

Weight hoisted, according to 
the old theory, 

lbs. 

C) r- 

OHOHilfllOHO 

cjoocaox^ctnc 

OrtWlOHJOffinOO 

— — O) 

Velocity of the weight as¬ 
cending, - 

feet. 

co »o 

to o to oi o 

to Ot L' (D ffl Q « O 

• • •••••• 

r—( t-H 

Velocity with which the wa¬ 
ter strikes the wheel in mo¬ 
tion, or relative velocity, - 

feet. 

CO 

CO 

CO 

OrjtcOOOOOHClifco 

' r—1 i-H t— 1 vH t-H 

Velocity of the wheel per se¬ 
cond, by supposition, 

feet. 

CO 

CO 

CO 

COOOODCOiflO^WO 

i—l t-H t-H 


4 ) 

I I 


Tj< CO 


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CHAP. II.] 


MECHANICS. 


63 


ARTICLE 35. 

NEW THEORY DOUBTED. 

Although I know that the velocity of the wheel, by 
this new theory, is, (though rather slow,) much nearer 
to general practice than by the old, yet I am led to doubt 
its correctness, for the following reasons; namely : 

There are 16 cubic feet of water, equal to 1000 lbs. 
expended in a second; which, multiplied by its perpen¬ 
dicular descent, 4 feet, produces the power 4000. The 
ratio of the power and effect by the old theory, is as 10 
to 1.47; and by the new, as 4 to 1, as appears in the 9th 
column of the scale: this is a proof that the old theory 
is incorrect, and sufficient to make us suspect that there 
is some error in the new. And as the subject is of the 
greatest consequence in practical mechanics, I therefore 
have endeavoured to discover a true theory, and will show 
my work, in order that if I establish a theory, it may be 
the easier understood, if right, or detected, if wrong. 


ARTICLE 36. 

ATTEMPT TO DEDUCE A TRUE THEORY. 

I constructed the apparatus fig. 18, Plate II., which 
represents a simple wheel with a rope passing over it, and 
the weight P, 100 lbs. at one end to act by its gravity, 
as a power to produce effects, by hoisting the weight w 
at the other end. 

This seems to be on the principles of the lever, and 
overshot wheel; but with this exception, that the quan¬ 
tity of descending matter, acting as power, will still be 
the same, although the velocity will be accelerated, 
whereas, in overshot wheels, the power on the wheel is 
inversely, as the velocity of the wheel. 

Here we must consider, 

1. That the perpendicular descent of the body P, per 
second, multiplied into its weight, shows the power. 

2. That the weight w, when multiplied into its per¬ 
pendicular ascent, gives the effect. 

3. That the natural velocity of the falling body P, is 16 



G4 


MECHANICS. 


[CHAP. II. 

feet the first second, and the distance it has to fall 1G 
feet. 

4. Xhat we suppose the weight w, or resistance, will 
occupy its proportional part of the velocity, that is, if w 
be = | P, the velocity with which P will then descend, 
will be h 1G = 8 feet per second. 

5. If w be = P, there can be no velocity, consequently 
no effect; and if w = o, then P will descend 1G feet in a 
second, but produce no effect, because the power, al¬ 
though 1G00 per second, is applied to hoist nothing. 

Upon these principles I have calculated the following 
scale. 


A scale for determining the maximum charge and velocity of 
100 lbs . descending by its gravity. 


►d 

3 

CT* 2 . 
73 CTQ 

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rf 

TJ 

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feet. 

feet. 

0 

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10 : 0 




1 

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15.84 

15.84 

1584 

10 : 0 




10 

1.6 

14.4 

144 

1440 

10 : 1 




20 

3.2 

12.8 

256 

1280 

10 : 2 




30 

4.8 

11.2 

336 

1120 

10 : 3 




40 

6.4 

9.6 

384 

960 

10 : 4 

Maximum, by 
new theory. 



50 

60 

8 . 

9.6 

8 . 

6.4 

400 

384 

800 

640 

10 :5 

10 : 6 



70 

11.2 

4.8 

336 

480 

10 :7 




80 

12.8 

3.2 

256 

320 

10 :8 




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14.4 

1.6 

144 

160 

10 = 9 




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15.84 

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10 : 99 


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MECHANICS. 


65 


CHAP. II.] 

By this scale it appears, that when the weight w is 
= 50 = § P the power, the effect is at a maximum, 
namely, 400, as appears in the 6th column, when the 
velocity is half the natural velocity, namely, 8 feet per 
second; and then the ratio of the power to the effect 
is as 10 to 5, as appears in the 8tli line. 

By this scale it appears, that all engines that are 
moved by one constant power, which is equably accele¬ 
rated in its velocity, must be charged with weight or 
resistance equal to half the moving power, in order to 
produce the greatest effect in a given time; but if time 
be not regarded, then the greater the charge, so as to 
leave any velocity, the greater the effect, as appears by 
the 8th column. So that it appears that an overshot 
wheel, if it be made immensely capacious, and to move 
very slowly, may produce effects in the ratio of 9.9 to 
10 of the power. 


ARTICLE 37. 

SCALE OF EXPERIMENTS. 

The following is a scale of actual experiments made 
to prove whether the resistance occupies its proportion 
of the velocity, in order that I might judge whether the 
foregoing scale was founded on true principles: the ex¬ 
periments were not very accurately performed, but were 
often repeated, and the results were always nearly the 
same. See Plate II. fig. 18. 



G6 


MECHANICS. [CHAP. II. 


A SCALE 


OF 

EXPERIMENTS. 


Power applied on the wheel, in pounds. 

Distance it had to descend, in feet. 

Weight, in pounds, hoisted the whole distance. 

Equal parts of time [each being two beats of a watch] in which the 
weight was hoisted the whole distance. 

Distance in feet, that the weight moved in one of the equal parts of 
time, found by dividing 40, the whole distance, by the number of 
equal parts of time taken up in the ascent. 

Effect, found by multiplying the weight of w into the velocity, or dis¬ 
tance ascended in one of those parts of time. 

Power, found by multiplying the weight of P into its descent, in one of 
those parts of time. 

Ratio of the power and effect. 

« 

Effect, supposing it to be as the square of the velocity of the weight; 
found by multiplying the weight into the square of its velocity. 

7 

40 

7 


0 

0 






6 

20 

2X6 

12 

14 

10:8.5 

24 



5 

15.5 

2.6x5 

13 

18.2 

10:7.1 

33 .8 



4 

12 

3.33x4 

13.32 

23.31 

10:5.7 

44 .35 

1 


3.5 

10 

4X3.5 

14 

28 

10:5. 

maximum 









new theory. 



3 

9 

4.44x3 

13.32 

31.08 

10:4.2 

59 .14 



2 

6.5 

6 X 2 

12 

42 

10:2.8 

72 maximum 



1 

6 

6.6 X 1 

6.6 

46.2 

10:1.4 

33 .56 



1 0 

5 

8 

0 

56 




















































MECHANICS. 


67 


CHAP. II.] 

By this scale it appears, that when the power P falls 
freely without any load, it descends 40 feet in five equal 
parts of time; but when charged with 3.5 lbs. = \ P, 
which was 7 lbs., it then takes up 10 of those parts of 
time to descend the same distance; which seems to show, 
that the charge occupies its proportional part of the 
whole velocity, which was wanted to be known, and the 
maximum appears as in the last scale. It also shows that 
the effect is not as the weight multiplied into the square 
of its ascending velocity, this being the measure of the 
effect that would be produced by the stroke on a non- 
elastic body. 

Atwood, in his Treatise on Motion, gives a set of ac¬ 
curate experiments, to prove (beyond doubt) that the 
conclusion I have drawn is right; namely:—That the 
charge occupies its proportional part of the whole velo¬ 
city- 

These experiments partly confirmed me in what I have 
called the New Theory; but still doubting, and after I 
had formed the foregoing tables, I called, for his assist¬ 
ance, on the late ingenious and worthy friend, William 
Waring, teacher in the Friends’ Academy, Philadelphia, 
who informed me that he had discovered the error in the 
old theory, and corrected it in a paper which he had laid 
before the Philosophical Society of Philadelphia, wherein 
he had shown that the velocity of the undershot water¬ 
wheel, to produce a maximum effect, must be just one 
half the velocity of the water. 


ARTICLE 38. 

WILLIAM WARING*S THEORY. 

The following are extracts from the above mentioned 
paper, published in the third volume of the transactions 
of the American Philosophical Society, held at Phila¬ 
delphia, p. 144. . 

After his learned and modest introduction, in which 
he shows the necessity of correcting so great an error as 



68 


MECHANICS. 


[CHAP. II. 


the old theory, he begins with these words; namely:— 
“But, to come to the point, I would just premise these 

DEFINITIONS. 

If a stream of water impinge against a wheel in mo¬ 
tion, there are three different velocities to be considered 
appertaining thereto; namely: 

1st. The absolute velocity of the water. 

2d. The absolute velocity of the wheel. 

3d. The relative velocity of the water to that of the 
wheel; that is, the difference of the absolute velocities, 
or the velocity with which the water overtakes or strikes 
the wheel. 

Now the mistake consists in supposing the momen¬ 
tum or force of the water against the wheel, to be in 
the duplicate ratio of the relative velocity; whereas: 


PROPOSITION i. 

The force of an invariable stream impinging against 
a mill-wheel in motion, is in the simple proportion of 
the relative velocity. 

For, if the relative velocity of a fluid against a single 
plane be varied either by the motion of the plane or of 
the fluid from a given aperture, or both, then the num¬ 
ber of particles acting on the plane, in a given time, and 
likewise the momentum of each particle being respec¬ 
tively as. the relative velocity, the force, on both these 
accounts, must be in the duplicate ratio of the relative 
velocity, agreeably to the common theory, with respect 
to this single plane; but the number of these planes, or 
parts of the wheel acted on in a given time, wflll be as 
the velocity of the wheel, or inversely as the relative ve¬ 
locity ; therefore, the moving force of the wheel must be 
as the simple ratio of the relative velocity. Q. E, D. 

Or, the proposition is manifest from this consideration, 
that while the stream is invariable, whatever be the ve¬ 
locity of the wheel, the same number of particles, or 
quantity of fluid, must strike it somewhere or other in a 
given time; consequently, the variation of the force is 




MECHANICS. 


69 


CHAP. II.] 


only on account of the varied impingent velocity of the 
same body, occasioned by a change of motion in the 
wheel; that is, the momentum is as the relative velocity. 

Now this true principle, substituted for the erroneous 
one in use, will bring the theory to agree remarkably 
with the notable experiments of the ingenious Smeaton, 
published in the Philosophical Transactions of the Royal 
Society of London, for the year 1751, vol. 51; for which 
the honorary annual medal was adjudged by the society, 
and presented to the author by their president. 

An instance or two of the importance of this correc¬ 
tion may be adduced, as follows: 


PROPOSITION II. 

The velocity of a wheel, moved by the impact of a 
stream, must be half the velocity of the fluid, to produce 
the greatest effect possible. 

f Y = the velocity, M = the momentum, of the fluid, 
j v — the velocity, P = the power, of the wheel. 
Then V—v = their relative velocity by definition 3d. 


And as Y: Y—v:: M : M x V—v = P, (Prop. 1,) which 

v 

xY=Pj=Mx Y v—v 3 = a maximum; hence Y V—v 2 = 

V 

a maximum, and its fluxion (v being a variable quan¬ 
tity) = Yv—2vv =. 0; therefore = | Y; that is, the ve¬ 
locity of the wheel = half that of the fluid, at the place 
of impact when the efiect is a maximum. Q. E. D. 

The usual theory gives v = j Y, where the error is 
not less than one-sixth of the true velocity. 

Wm. Waring.’' 

Philadelphia , Ith^ 

9th mo. 1790. j 




TO 


MECHANICS. 


[chap. II. 

I here omit quoting Proposition III. as it is altogether 
algebraical, and refers to a figure. I am not writing for 
men of science, but for practical mechanics. 


ARTICLE 39. 

Extract from a further paper, read in the Philosophical 

Society, April bth, 1793 . 

“ Since the Philosophical Society were pleased to fa¬ 
vour my crude observations on the theory of mills with 
a publication in their transactions, I am apprehensive 
some part thereof may be misapplied; it being therein 
demonstrated, that ‘the force of an invariable stream im¬ 
pinging against a mill-wheel in motion, is in the simple 
direct ratio of the relative velocity.’ Some may suppose 
that the effect produced should be in the same proportion, 
and either fall into an error, or finding by experiment, 
the effect to be as the square of the velocity, conclude the 
new theory to be not well founded; I therefore wish 
there had been a little added, to prevent such misapplica¬ 
tion, before the Society had been troubled with the read¬ 
ing of my paper on that subject, perhaps something like 
the following. 

The maximum effect of an undershot wheel, produced 
by a given quantity of water, in a given time, is in the 
duplicate ratio of the velocity of the water; for the effect 
must be as the impetus acting on the wheel, multiplied 
into the velocity thereof: but this impetus is demon¬ 
strated to be simply as the relative velocity, Proposition 
I., and the velocity of the wheel, producing a maximum, 
being half of the water, by Proposition II., is likewise as 
the velocity of the water; hence the power acting on the 
wheel multiplied into the velocity of the wheel, or the 
effect produced, must be in the duplicate ratio of the ve¬ 
locity of the water. Q. E. D. 

Corollary. Hence the effect of a given quantity of 
water, in a given time, will be as the height of the head, 
because this height is as the square of the velocity. This 
also agrees with experiment. 




MECHANICS. 


71 


CHAP. II.] 

If the force, acting on the wheel, were in duplicate 
ratio of the water’s velocity, as is usually asserted, then 
the effect would he as the cube thereof, when the quan¬ 
tity of water and time are given, which is contrary to 
the result of experiment.” 


ARTICLE 40. 
waring’s theory doubted. 

From the time I first called on William Waring, until 
I read his publication on the subject (after his death,) I 
had rested partly satisfied with the new theory, as I 
have called it, with respect to the velocity of the wheel, 
at least; but finding that he had not determined the 
charge, as well as the velocity, by which we might have 
compared the ratio of the power and the effect produced, 
and that he had assigned somewhat different reasons for 
the error, and having found the motion to he rather too 
slow to agree with practice, I began to suspect the whole, 
and resumed the search for a true theory; thinking that 
perhaps no person had ever yet considered every thing 
that affects the calculation; I therefore premised the fol¬ 
lowing 


POSTULATES. 

1. A given quantity of perfectly elastic, or solid mat¬ 
ter, impinging on a fixed obstacle, its effective force is 
as the squares of its different velocities, although its in¬ 
stant force may he as its velocities simply; because the 
distance it will recede after the stroke through any re¬ 
sisting medium, will be as the squares of its impinging 
velocities. 

2. An equal quantity of elastic matter, impinging on a 
fixed obstacle with a double velocity, produces a quad¬ 
ruple effect, their effects are as the squares of their velo¬ 
cities. Consequently— 

3. A double quantity of said matter, impinging with a 



MECHANICS. 



[CHAP. II. 


double velocity, produces an octuple effect, or their ef¬ 
fects are as the cubes of their velocities, Art. 47 and 07. 

4. If the impinging matter be non-elastic, such as 
fluids, then the instant force will be but half, but the 
ratio will be the same in each case. 

5. A double velocity, through a given aperture, gives 
a double quantity to strike the obstacle or wheel; there¬ 
fore the effects will be as the cubes of the velocity. See 
Art. 47. 

6. But a double relative velocity cannot increase the 
quantity that is to act on the wheel; therefore, the ef¬ 
fect can only be as the square of the velocity, by postu¬ 
late 2. 

7. Although the instant force and effects of fluids 
striking on fixed obstacles, are only as their simple velo¬ 
cities, yet their effects on moving wheels, are as the 
squares of their velocities; because, 1st, a double striking 
velocity gives a double instant force, which bears a dou¬ 
ble load on the wheel; and 2d, a double velocity moves 
the load a double distance, in an equal time, and a 
double load moved a double distance, is a quadruple 
effect. 


ARTICLE 41. 

SEARCH FOR A TRUE THEORY, COMMENCED ON A NEW PLAN. 

It appears that we have applied wrong principles in 
our search after the true theory of the maximum velocity, 
and load of undershot wheels, or other engines moved 
by a constant power, that does not increase or decrease 
in quantity on the engine, as on an overshot water¬ 
wheel, as the velocity varies. 

Let us suppose water to issue from under a head of 
16 feet, on an undershot water-wheel; then, if the wheel 
move freely with the water, its velocity will be 32.4 feet 
per second, but will bear no load. 

Again; suppose we load it, so as to make its motion 
equal only to the velocity of water spouting from under 
a head of 15 feet; it appears evident that the load will 



MECHANICS. 


CHAP. II.] 



then be just equal to the 1 foot of the head, the velocity 
of which is checked; and this load multiplied into the 
velocity of the wheel; namely: 31.34 x 1 = 31.34, for 
the effect. 

This appears to be the true principle, from which we 
must seek the maximum velocity and load, for such en¬ 
gines as are moved by one constant power; and on this 
principle I have calculated the following scale. 


A scale for determining the true maximum velocity and load 

for undershot ivheels. 


H 

3 





o 

? 

CD 

P 

(~ 

'TO ^ 

P 

< CP 

CD 

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B 

o ^ 

C. < 

elocity of 
cond, bei 
the water 
unbalanc 

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p 

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3 ~ O 

CD Cr* 

3“ cr cd 

fleet per 
city of tl 
the load. 


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p 1- 

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feet. 

feet. 

feet. 




16 

16 

32.4 

0 

0 



15 

31.34 

1 

31.34 



14 

30.2 

2 

60.4 



12 

28 

4 

112 



10 

25.54 

6 

153.24 



8 

22.8 

8 

182.4 



7 

21.43 

9 

192.87 



6 

19.84 

10 

198.4 



5.66 

19.27 

10.33 

198.95 



5.33 

18 . 71 ' 

10.66 

199.44 

Maximum mo- 


5 

18 

11 

198 

tion and. load. 


4 

16.2 

12 

194.4 



3 

14 

13 

172 



2 

11.4 

14 

159.6 



1 

8.1 

15 

120 



0 

0 

16 

0 









































74 


MECHANICS. 


[CHAP. II. 

Iii this scale let us suppose the aperture of the gate 
to be a square foot; then the greatest load that will ba¬ 
lance the head will be 1G cubic feet of water, and the 
different loads will be shown in cubic feet of water. 

It appears by this scale, that when the wheel is loaded 
with 10.66 cubic feet of water, just f of the greatest 
load, its velocity will be 18.71 feet per second, just .577 
parts of the velocity of the water, and the eftect pro¬ 
duced is then at a maximum, or the greatest possible, 
namely: 199.44. 

To make this more plain, let us suppose A B, Plate 
II. fig. 19, to be a fall of water of 16 feet, which we 
wish to apply to produce the greatest effect possible, by 
hoisting water on its side, opposite to the power applied. 
First, on the undershot principle, where the water acts 
by its impulse only. Let us suppose the water to strike 
the wheel at I, then, if we let the wheel move freely with¬ 
out any load, it will move with the velocity of the water, 
namely, 32.4 feet per second, but will produce no effect, 
if the water issue at C; although there be 32.4 cubic feet 
of water expended, under 16 feet perpendicular descent . 
Let the weight of a cubic foot of water be represented by 
unity or 1, for ease in counting; then 32.4 X 16 will show 
the power expended, per second, namely, 518.4; and the 
water it hoists multiplied into its perpendicular ascent, or 
height hoisted, will show the effect. Then, in order to 
obtain effect from the power, we load the wheel; the sim¬ 
plest way of doing which, is, to cause the tube of water C 
D to act on the back of the bucket at I; then, if C D be 
equal to A B, the wheel will be held in equilibrio: this is 
the greatest load, and the whole of the fall A B is ba- 
lanced, and no part left to give the wheel velocity; there¬ 
fore the effect = o. But if we make C D = 12 feet of A B, 
then from 4 to A, =: 4 feet, is left unbalanced, to give ve¬ 
locity to the wheel, which being loaded with 12 feet, 
would be exactly balanced by 12 on the other side, and 
left perfectly free to move either way by the least force 
applied beyond this balance. Therefore it is evi¬ 
dent, that the whole pressure or force of 4 feet of A B 
will act to give velocity to the wheel, and, as there is 


MECHANICS. 


75 


CHAP. II.] 

no resistance to oppose tlie pressure of these 4 feet, the 
velocity will be that of water spouting from under a 4 
feet head, namely, 16.2 feet per second, which is shown 
by the horizontal line, 4 = 16.2 and the perpendicular 
line 12 = 12, represents the load of the wheel; the rec¬ 
tangle or product of these two lines form a parallelogram, 
the area of which is a true representation of the effect, 
namely, the load 12 multiplied into 16.2, the distance it 
moves per second = 194.4, the effect. In like manner we 
may try the effect of different loads; the less the load, the 
greater will be the velocity. The horizontal lines ail 
show the velocity of the wheel, produced by the respec¬ 
tive heads left unbalanced, and the perpendicular lines 
show the load on the wheel; and we find that when the 
load is 10.66 = § 16, the load at equilibrio, the velocity of 
the wheel will be 18.71jeet per second,which is—-g-parts, 
or a little less than 6 tenths or § the velocity of the water, 
and the effect is 199.44, the maximum, or greatest possi¬ 
ble; and if the aperture of the gate be 1 foot, the quan¬ 
tity will be 18.71 cubic feet per second. The power be¬ 
ing 18.71 cubic feet expended per second, multiplied by 
16 feet of the perpendicular descent, produce 299.36, 
the ratio of the power and effect, being as 10 to 6, t 8 q, or 
nearly as 3 : 2; but this is supposing none of the force 
lost by non-elasticity. 

This may appear plainer, if we suppose the water to 
descend in the tube A B, and, by its pressure, to raise 
the water in the tube C D; for it is evident, that if we 
raise the water to D, we have no velocity, therefore, 
effect = o. Then again, if we open the gate at C, we 
have 32.4 feet per second velocity; but because we do 
not hoist the water to anv height, effect is = o. There- 
fore, the maximum is somewhere between C and D. 
Then suppose we open gates of 1 foot area, at different 
heights, the velocity will show the quantity of cubic 
feet raised; which multiplied by the perpendicular 
height of the gate from C, or height raised, gives the 
effect, and the maximum as before. But here we must 
consider that in both these cases the water acts as a 
perfectly definite quantity, which will produce effects 


70 


MECHANICS. 


[CIIAP. II. 

equal to elastic bodies, or equal to its gravity, (see Art. 
59,) which is unattainable in practice; whereas, when it 
acts by percussion only, it communicates only hall ol its 
original force, on account of its non-elasticity, the other 
half being spent in splashing about; therefore, the true 
effect will be T W ( a little more than 4) of the moving 
power: because nearly 4 is lost to obtain velocity, and 
half of the remaining 4 is lost by non-elasticity. These 
are the reasons why the effect produced by an undershot 
wheel is only half of that produced by an overshot wheel, 
the perpendicular descent and quantity of water being 
equal. And this agrees with Smeaton’s experiments, 
(see Art. 68;) but if avc suppose the velocity of the wheel 
to be 4 that of the water = 10.8, and the load to be 4 
of 16, the greatest load at equilibrio, \\diich is = 7.111, 
as by old theory, then the effect will be 10.8 x 4.9 of 16 
= 76.79 for the effect, which is quite too little, the moving 
poAver being 32.4 cubic feet of Avater multiplied by 16 
feet descent = 518.4; the effect by this theory being less 
than T Vo °f ^ ie poAver, about half equal to the effect, by 
experiment, which effect is set 011 the outside of the dot¬ 
ted circle in fig. 19. The dotted lines join the corner of 
the parallelograms, formed by the lines that represent 
the loads and velocities, in each experiment or supposi¬ 
tion, the areas of Avhich truly represent the effect, and 
the dotted line A a d x, meeting the perpendicular line 
x E in the point x, forming the parallelogram A B C x; 
truly represents the power = 518.4. 

Again, if we suppose the wheel to move with half the 
A'docity of the A\ r ater, namely, 16.2 feet per second, and 
to be loaded with half the greatest load = 8, according to 
Waring’s theory; then the effect Avill bel6.2xS = 129.6 
for the effect, about 4W of the poAA r er, which is still less 
than by experiment. All this seems to confirm the 
maximum brought out on the neAv principles. 

But, if AA T e suppose, according to the neAv principle, 
that when the Avlieel moves with the velocity of 16.2 
feet per second, which is the A^elocity of a four feet head, 
it will then bear as a load the remaining tAvelve feet, then 
the effect Avill be 16.2 x 12 = 194.4, AA r hich nearly agrees 


MECHANICS. 


77 


CHAP. II.] 

with practice; but as most mills in practice move faster, 
and few slower, than what I call the true maximum, this 
shows it to be nearest the truth: the true maximum 
velocity being .577 of the velocity of the water, and the 
mills in practice moving with §, and generally quicker.* 
This scale also establishes a true maximum charge for 
an overshot wheel; that is, if we suppose the power, 
or quantity of water on the wheel at once, to be always 
the same, even although the velocity vary, which would 
be the case if the buckets were always kept full; for, 
suppose the water to be shot into the wheel at a, and 
by its gravity to raise the whole water again on the op¬ 
posite side; then as soon as the water rises in the wheel 
to d, it is evident that the wheel will stop, and the ef¬ 
fect bb = o; therefore, we must let the water out of the 
wheel before it rises to d, which will be, in effect, to lose 
part of the power to obtain velocity. If the buckets, both 
descending and ascending, carry a column of water one 
foot square, then the velocity of the wheel will show the 
quantity hoisted as before, which multiplied by the per¬ 
pendicular ascent, shows the effect; and the quantity 
expended multiplied by the perpendicular descent, shows 
the power; and we find that when the wheel is loaded 
with | of the power, the effect will be at a maximum; 
that is, the whole of the water is hoisted -§ of its whole 


* The reason why the wheel bears so great a load at a maximum, appears to be 
as follows; namely:— 

A 16 feet head of w T ater over a gate of 1 foot, issues 32.4 cubic feet of water in 
a second, to strike the wheel in the same time that a heavy body will take up 
in falling through the height of the head. Now, if 16 cubic feet of elastic matter 
were to fall 16 feet, and strike an elastic plane, it -would rise by the force of the 
stroke to the height from whence it fell, or, in other words, it will have force 
sufficient to bear a load of 16 cubic feet. 

Again, if 32 cubic feet of non-elastic matter, moving w r ith the same velocity 
(with which the 10 feet of elastic matter struck the plane,) strike a wheel in the 
same time, although it communicate only half the force that gave it motion; yet 
because there is a double quantity striking in the same time, the effects will be 
equal; that is, it will bear a load of 16 cubic feet, or the whole column to-hold 
it in equilibrio. 

Again, to check the whole velocity, requires the whole column that produces 
the velocity; consequently, to check any part of the velocity, will require such 
a part of the column, as is equal to the part checked; and we find by Art. 41, 
that, to check the velocity of the wheel, so as to be .577 of the velocity of the 
water, it requires 2-3ds of the wdrole column, and this is the maximum load. 
When the velocity of the wheel is multiplied by 2-3ds of the column, it produces 
the effect, which wdll be to the power, as 38 to 100 ; or, as 3.8 to 10, somewdrat 
more than l-3d, and the friction and resistance of the air may reduce it to l-3d. 


78 


M E C H A N IC S . 


[CHAP. II. 

descent; or •§ of the water, the whole of the descent; 
therefore, the ratio of the power to the effect is as 3 to 2, 
or double the effect of an undershot wheel: but this is 
supposing the quantity in the buckets to be always the 
same, whereas, in overshot wheels, the quantity in the 
buckets is inversely as the velocity of the wheel; that 
is, the slower the motion of the wheel, the greater the 
quantity in the buckets; and the greater the velocity, 
the less the quantity: but again, as we are obliged to 
let the overshot wheel move with a considerable velo¬ 
city, in order to obtain a steady, regular motion to 
the mill, we shall find this charge to be always nearly 
right; hence, I deduce the following theory. 


ARTICLE 42. 

TII E 0 R Y. 

A TRUE THEORY DEDUCED. 

This scale seems to have shown: 

1. That when an undershot mill moves with .577 or 
nearly .6 of the velocity of the water, it will then bear a 
charge equal to f of the load that will hold the wheel in 
equilibrio, and then the effect will be at a maximum. 
The ratio of the power to the effect will be as 3 to 1, 
nearly. 

2. That when an overshot wheel is charged with -§ of 
the weight of the water acting upon the wheel, then the 
effect will be at a maximum; that is, the greatest effect 
that can be produced by said power in a given time, 
and the ratio of the power to the effect will be as 3 to 2, 
nearly. 

3. That | of the power is necessarily lost to obtain 
velocity, or to overcome the inertia of the matter; and 
this will hold true with all machinery that requires ve¬ 
locity as well as power. This I believe to be the true 
theory of water-mills, for the following reasons, namely: 

1. The theory is deduced from original reasoning, 
without depending much on calculation. 



CHAP. II.] MECHANICS. 79 

2. It agrees better than any other theory with the in¬ 
genious Smeaton’s experiments. 

3. It agrees best with real practice, according to the 
best of my information. 

Yet I do not wish any person to receive it implicitly, 
without first informing himself whether it be well 
founded, and in accordance with actual experience: for 
this reason I have quoted the experiments of Smeaton 
at full length, in this work, that the reader may com¬ 
pare them with the theory. 


TRUE THEOREM FOR FINDING THE MAXIMUM CHARGE FOR UNDER¬ 
SHOT WHEELS. 

As the square of the velocity of the water, or wheel 
empty, is to the height of the head, or pressure, which 
produced that velocity, so is the square of the velocity 
of the wheel loaded, to the head, pressure, or force, 
which will produce that velocity; and this pressure de¬ 
ducted from the wdiole pressure or force, will leave the 
load moved by the wheel, on its periphery or verge, 
which load, multiplied by the velocity of the wheel, 
shows the effect. 


PROBLEM. 

Let V = 32.4, the velocity of the water or wheel, 

P = 16, the pressure, force, or load, at equilibrio, 
v = the velocity of the wheel, supposed to be 16.2 
feet per second, ' 

p = the pressure, force, or head, to produce said 
velocity, 

1 — the load on the wheel, 

Then, to find 1, the load, we must first find p; 
Then, by 

Theorem YY : P : : vv : p. 

And P—p = 1 
YY p = vvP 
vvP 

P = — = 4 

YY 

1 = P—p = 12, the load. 


80 


MECHANICS. 


[CHAP. II. 

Which, in words at length, is the square of the velocity 
of the wheel multiplied by the whole force, pressure, or 
head of the water, and divided by the square ol the 
velocity of the water, quotes the pressure, force, or head 
of water that is left unbalanced by the load to produce 
the velocity of the wheel; which pressure, force, or head, 
subtracted from the whole pressure, force, or head, 
leaves the load that is on the wheel. 


ARTICLE 43. 

Theorem for finding the velocity of the wheel when ive have 
the velocity of the water , load at equilibria, and load on the 
wheel given. 

As the square root of the whole pressure, force, or 
load at equilibrio, is to the velocity of the water, so is 
the square root of the difference, between the load on 
the wheel and the load at equilibrio, to the velocity of 
the wheel. 


PROBLEM. 

Let V = velocity of the water = 32.4, 

P = pressure, force, head or load at equilibrio = 
16,1 = the load on the wheel, suppose 12, 
v = velocity of the wheel, 

Then by the 

Theorem y/P : V : : y/P —1 : v 

And y/P x v = V y/P— 1 : v 
Vy/P— 1 

1 =— = — = 16.2 f The velocity of 
v/P \ the wheel. 

That is, in words at length, the velocity of the water, 
32.4 multiplied by the square root of the difference, be¬ 
tween the load on the wheel, 12, and the load at equili¬ 
brio, 16 = 2 = 64.8 divided by the square root of the load 
at equilibrio, quotes 16.2, the velocity of the wheel. 

Now, if we seek for the maximum by either of these 
theorems, it will be found as in the scale, fig. 19. 






M E CIIA NI C S. 


81 


CHAP. II.] 

Perhaps here may now appear the true cause of the 
error in the old theory, Art. 34, by supposing the load 
on the wheel to be as the square of the relative velocity 
of the water and wheel. 

And of the error in what I have called the new the¬ 
ory? by supposing the load to be in the simple ratio of 
the relative or striking velocity of the water, Art. 38; 
whereas, it is to be found by neither of these proportions. 

Neither the old nor the new theory agrees with prac¬ 
tice ; therefore we may suspect they are both founded 
in error. 

But if what I call the true theory should be found to 
accord with experience, the practitioner need not be 
much concerned on what it is founded. 


ARTICLE 44. 

Of the maximum velocity for overshot wheels , or those that 
are moved by the weight of the water. 

Before I dismiss the subject of maximums, I think it 
best to consider whether this doctrine will apply to the 
motion of the overshot wheel. It seems to be the gene¬ 
ral opinion of those who consider the matter, that it will 
not; but that the slower the wheel moves, provided it be 
capacious enough to hold all the water, without losing 
any until it be delivered at the bottom of the wheel, the 
greater will be the effect, which appears to be the case 
in theory, (see Art. 36;) but how far this theory will hold 
good in practice is to be considered. Having met with 
the ingenious James Smeaton’s experiments, where he 
shows that when the circumference of his little wheel, 
of 24 inches diameter, (head 6 inches) moved with about 
3.1 feet per second (although the greatest effect was di¬ 
minished about ~o of fhe whole) he obtained the best ef¬ 
fect with a steady, regular motion. Hence he concludes 
about three feet to be the best velocity for the circum¬ 
ference of overshot mills. See Art. 68. 1 undertook to 
compare this theory of his with the best mills in practice. 

6 



82 


MECHANICS. 


[CHAP. II. 

and finding that those of about 17 feet diameter general¬ 
ly moved about 9 feet per second, being treble the velo¬ 
city assigned by Smeaton, I began to doubt the theory, 
which led me to inquire into the principle that moves an 
overshot wheel; and this I found to be that of a body de¬ 
scending by its gravity, and subject to all the laws ol fall¬ 
ing bodies, (Art. 10,) or of bodies descending inclined 
planes and curved surfaces, (Art. 11;) the motion being 
equably accelerated in the whole of its descent, its veloci¬ 
ty being as the square root of the distance descended 
through; and that the diameter of the wheel was the 
distance through which the water descended. From 
thence I concluded that the velocity of the circumfe¬ 
rence of overshot wheels was as the square root of their 
diameters, and of the distance the water has to descend, 
if it be a breast or a pitch-back wheel: then, taking 
Smeaton’s experiments, with his wheel of two feet dia¬ 
meter, for a foundation, I say, as the square root of the 
diameter of Smeaton’s wheel is to its maximum veloci¬ 
ty, so is the square root of the diameter of any other 
wheel to its maximum velocity. Upon these principles 
I have calculated the following table, and having com¬ 
pared it with at least 50 mills in practice, find it to 
agree so nearly with all those best constructed, that I 
have reason to believe it is founded on true principles. 

If an overshot wheel move freely, without resistance, 
it will acquire a mean velocity between that of the wa¬ 
ter coming on the wheel, and the greatest velocity it 
would acquire by falling freely through its whole de¬ 
scent: therefore, this mean velocity will be greater than 
the velocity of the water coming on the wheel; conse¬ 
quently, the backs of the buckets will overtake the wa¬ 
ter, and drive a great part of it out of the wheel. But 
the velocity of the water being accelerated by its gra¬ 
vity, overtakes the wheel, perhaps half way down, and 
presses on the buckets until it leaves the wheel; there¬ 
fore the water presses harder upon the buckets in the 
lower than in the upper quarter of the wheel. Hence, 
appears the reason why some wheels cast their water; 
which is always the case when the head is not sufficient 


MECHANICS. 


83 


CHAP. II.] 

to give it velocity enough to enter the buckets. But 
this depends also much on the position of the buckets, 
and the direction of the sliute into them. It, however, 
appears evident that the head of water above the wheel 
should be nicely adjusted to suit the velocity of the 
wheel. Here we may consider that the head above the 
wheel acts by percussion, or on the same principles with 
the undershot wheel; and, as we have shown, (Art. 40,) 
that the undershot wheel should move with nearly |ds 
of the velocity of the water, it appears that we should 
allow a head over the wheel that will give such velocity 
to the water, as will be to that of the wheel, as 3 to 2. 
Thus, the whole descent of the water of a mill-seat 
should be nicely divided between head and fall, to suit 
each other, in order to obtain the best effect, and a 
steady-moving mill. First, find the velocity with which 
the wheel will move, by the weight of the water, for any 
diameter you may suppose you will take for the wheel, 
and divide said velocity into two parts; then try if your 
head be such as will cause the water to come on with a 
velocity of 3 such parts, making due allowances for the 
friction of the water, according to the aperture', see Art. 
55. Then, if the buckets and the direction of the sliute 
be right, the wheel will receive the water well, and move 
to the best advantage, keeping a steady, regular motion 
when at work, loaded or charged, with a resistance equal 
to two-thirds of its power. Arts. 41,42. 


84 MECHANICS. [CHAP. II. 

A TABLE 

OF 

VELOCITIES OF THE CIRCUMFERENCE 

OF 

OVERSHOT WHEELS 

Suitable to their Diameters, or rather to the Fall, after the Water strikes 
the Wheel; and of the head of Water above the Wheel, suitable to said 
Velocities; also of the Number of Revolutions the Wheel will perform 
in a Minute, when rightly charged. 







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4 

5 

6 

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9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 
21 

22 

23 

24 

25 

26 

27 

28 

29 

30 


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S 

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3 

elocity o 
in feet 
cond. 

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1.51 

14.3 

6.92 

1.64 

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1.74 

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7.24 

1.84 

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1.94 

12.6 

7.57 

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7.86 

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11.54 

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2.74 

11.17 

8.47 

2.49 

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2.99 

10.78 

8.76 

2.68 

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3.28 

10.4 

9 . 

2.8 

.7 

3.5 

10.1 

9.28 

3 . 

.8 

3.8 

9.8 

9.5 

3.13 

.9 

4.03 

9.54 

9.78 

3.34 

1 . 

4.34 

9.3 

10 . 

3.49 

1.05 

4.54 

9.1 

10.28 

3.76 

1.1 

4.86 

8.9 

10.5 

3.84 

1.15 

4.99 

8.7 

10.7 

3.97 

1.2 

5.27 

8.5 

10.95 

4.2 

1.25 

5.45 

8.3 

11.16 

4.27 

1.3 

5.57 

8.19 

11.36 

4.42 

1.35 

5.77 

8.03 

11.54 

4.56 

1.4 

5.96 

7.93 

11.78 

4.7 

1.45 

6.15 

7.75 

11.99 

4.9 

1.5 

6.4 

7.63 


\ 
























MECHANICS. 


85 


CHAP. II.] 

This doctrine of maximums is very interesting, and 
is to be met with in many occurrences through life. 

1. It has been shown that there is a maximum load 
and velocity for all engines, to suit the power and velo¬ 
city of the moving power. 

2. There is also a maximum size, velocity and feed 
for mill-stones, to suit the power: a maximum velocity 
for rolling-screens and bolting-reels, by which the great¬ 
est work can be done in the best manner, in a given 
time. 

3. A maximum degree of perfection and closeness, 
with which grain is to be manufactured into flour, so as 
to yield the greatest profit by the mill in a day or week, 
and this maximum is continually changing with the 
prices in the market, so that what would be the greatest 
profit at one time, will sink money at another. See 
Art. 113. 

4. A maximum weight for mallets, axes, sledges, &c., 
according to the strength of those that use them. 

A true attention to the principles of maximums will 
prevent us from running into many errors. 


8G 


[chap. hi. 



CHAPTER III. 

HYDRAULICS. 

PRELIMINARY REMARKS. 

The science which treats upon the mechanical pro¬ 
perties and effects of water and other fluids, has most 
commonly been divided into two branches, Hydrosta¬ 
tics and Hydraulics. Hydrostatics treats of the weight, 
pressure and equilibrium of fluids, when in a state of 
rest. Hydraulics treats of water in motion, and the 
means of raising, conducting, and using it for moving 
machinery, or for other purposes. These two divisions 
are so intimately connected with each other, that the 
latter could not be at all understood without an acquaint¬ 
ance with the former; and it is not necessary, in a work 
like the present, to treat of them separately. Considered 
abstractly, the same laws obtain in the pressure and 
motion of water, as those which belong to solid bodies; 
and in the last chapter on Mechanics, this similarity has 
led to some notice of the effects produced by water, 
which, strictly speaking, would belong to the present. 
In doing this, utility has been preferred to a strict ad¬ 
herence to system. 

In treating of the elementary principles of Hydrau¬ 
lics, it is necessary to proceed upon theoretical prin¬ 
ciples : but let it always be recollected that from various 
causes resulting from the constitution of fluids, and par¬ 
ticularly from that essential property in them, the per¬ 
fect mobility of their particles among each other, the 
phenomena actually exhibited in nature, or in' the pro¬ 
cesses of art, in which the motion of water is concerned, 
deviate so very considerably from the deductions of the¬ 
ory, that the latter must be considered as a very imper¬ 
fect guide to the practical mill-wright and engineer. It 



87 


CHAP. III.] HYDRAULICS. 

is not to be inferred from this circumstance, that such 
theoretical investigations are false and useless; they are 
still approximations, which serve as guides to a certain 
extent. Their defectiveness arises from our inability to 
form an estimate of the many disturbing causes which 
influence the motion of fluids; whilst in the mechanics 
of solids we have, in many cases, no other correction to 
make in our theoretical deductions, than to allow for the 
effect of friction. 

“ The only really useful method of treating a branch 
of knowledge so circumstanced, is to accompany a very 
concise account of such general principles as are least 
inapplicable to practice, by proportionately copious de¬ 
tails of the most accurate experiments which have been 
instituted, with a view to ascertain the actual circum¬ 
stances of the various phenomena.” (Lctrdners Hydro¬ 
statics.) Such has been the course pursued, to a conside¬ 
rable extent, by the author of this work, and in pursu¬ 
ing this subject, under the present head of Hydraulics, 
we shall consider only such parts of the science as im¬ 
mediately relate to our purpose, namely, such as may 
lead to the better understanding of the principles and 
powers of water, acting on mill-wheels, and conveying 
water to them. 

^ - 


ARTICLE 45. 

OF SPOUTING FLUIDS. 

Spouting fluids observe the following laws: 

1. Their velocities and powers, under equal pressures, 
or equal perpendicular heights, and equal apertures, are 
equal in all cases.* 

2. Their velocities, under different pressures or per¬ 
pendicular heights, are as the square roots of those pres- 

* It makes no difference whether the water stands perpendicularly or inclined 
above the aperture, [see Plate III. fig 22,] provided the perpendicular height 
be the same; or whether the quantity be great or small, provided it be sufficient 
to keep the fluid up to the same height. 



88 


HYDRAULICS. 


[CHAP. III. 

sures, or heights, and their perpendicular heights, or 
pressures, are as the squares of their velocities.* * * § 

3. Their quantities expended through equal aper¬ 
tures, in equal times, under unequal pressures, are as 
their velocities simply.t 

4. Their pressures or heights being the same, their 
effects are as their quantities expended.J 

5. Their quantities expended being the same, their 
effects are as their pressure, or height of their head di¬ 
rectly^ 

G. Their instant forces with equal apertures, are as 
the squares of their velocities, or as the height of their 
heads directly. 

7. Their effects are as their quantities multiplied 
into the squares of their velocities.|| See Art. 4G. 

8. Therefore, their effects or powers with equal aper¬ 
tures, are as the cubes of their velocities.If 


* This law is similar to the 4th law of falling bodies, their velocities being as 
the square root of their spaces passed through; and by experiment it is known, 
that water will spout from under a four feet head, with a velocity of 16.2 feet per 
second, and from under a 16 feet head, 32.4 feet per second, which is only double 
to that of a 4 feet head, although there be a quadruple pressure. Therefore, by 
this law, we can find the velocity of water spouting from under any given head : 
for as the square root of 4, equal 2, is to 16.2, its velocity, so is the square root 
of 16, equal 4, to 32.4 its velocity. And again, as 16.2 squared, is to 4 its 
head, so is 32.4 squared, to 16, its head; by which ratio we can find the 
head that will produce any velocity. 

f It is evident that a double velocity will vent a double quantity. 

} If the pressure be equal, the velocity must be equal; and it is evident thaf’ : 
double quantity, with equal velocity, will produce a double effect. 

§ That is, if we suppose 16 cubic feet of water to issue from under a 4 feet 
head in a second, and an equal quantity to issue in the same time from under a 
16 feet head, then their effects will be as 4 to 16. But we must note, that the 
aperture in the last case must be only half of that in the first, as the velocity 
will be double. 

|| This is evident from this consideration; namely; that a quadruple impulse 
is required to produce a double velocity, by law 2d, where the velocities are as 
the square roots of their heads : theref^e their effects must be as the squares of 
their velocities. 

The effects of striking fluids with equal apertures are as the cubes of their 
velocities, for the following reasons, namely: 1st. If an equal quantity strike 
with double velocity, the effect is quadruple on that account by the 7th law; 
and a double velocity expends a double quantity by 3d law; therefore, the effect 
is augmented to the cube of the velocity.—The theory for undershot wheels 
agrees with this law also. 


HYDRAULICS. 


CHAP. III.] 

9. Tlieir velocity, under any head, is equal to the ve¬ 
locity that a heavy body would acquire in falling from 
the same height.* 

10. Their velocity is such, under any head or height, 
as will pass over a distance equal to twice the height of 
the head, in a horizontal direction, in the time that a 
heavy body falls the distance of the height of the head. 

11. Their action and reaction are equal:f 

12. They being non-elastic, communicate only half 
their real force by impulse, in striking obstacles; but by 
their gravity produce effects equal to elastic or solid 
bodies.J 


A SCALE, 

Founded on the 3d, Gth, and 7th laws, showing the effects of striking Fluids 

with different Velocities. 


Aperture, 

Multiplied by the 

Velocity 

Is equal the 

Quantity expended, 

Which multiplied by 
the 

Square of the velocity, 

Is equal the 

Effect, 

Which is as the 

Cubes of the velocity, 

1 

X 

1 

= 

1 

X 

1 

= 

1 

as 

1 

1 j 

X 

2 

= 

2 

X 

4 

— 

8 

as 

8 

1 | 

X 

3 

= 

3 

X 

9 

= 

27 

as 

27 

1 

X 

4 

= 

4 

X 

1 1* 
1(> 

= 1 

64 

as 

64 


* The falling body is acted on by the whole force of its own gravity, in the 
whole of its descent through any space; and the whole sum of this action that 
is acquired as it arrives at the lowest point of its fall is equal to the pressure of 
the whole head or perpendicular height above the issue; therefore their veloci¬ 
ties are equal. 

f That is, a fluid reacts back against the penstock with the same force that 
it issues {.gainst the obstacle it strikes; this is the principle by which Barker’s 
mill, and all those that are denominated improvements thereon, move. 

J When non-elastic bodies strike an obstacle, one half of their force is spent 
in a latera' direction, in changing their figure or in splashing about. See Art. 9. 

For wart of due consideration or knowledge of th is principle, many have been 
the errors committed by applying water to act by impulse, when it would have 
produced a double effect by its gravity. 


































































90 


hydraulics. 


[chap. hi. 


ARTICLE 4G. 

DEMONSTRATION OF THE SEVENTH LAW OF SPOUTING FLUIDS. 

Let A F. (plate III. fig. 26,) represent a head of water 1C feet high, 
and suppose it divided into 4 different heads of 4 feet each, as B C D 
E; then suppose we draw a gate of 1 foot square at each head succes¬ 
sively, always sinking the water in the head, so that it will be but 4 
feet above the centre of the gate in each case. 

Now it is known that the velocity under a 4 feet head is lb.2 feet 
per second; to avoid fractions say 16 feet, which will issue 16 cubic 
feet of wdter per second; and for sake of round numbers, let unity or 
1 represent the quantity of a cubic foot of water; then, by the 7th law 
the effect will be as the quantity multiplied by the square of the ve¬ 
locity; that is, 16 multiplied by 16 is equal to 256, which multiplied 
by 16, the quantity, is equal to 4096, the effect of each 4 feet head, 
and 4096 multiplied by 4 is equal to 16384, for the sum of effects of 
all the 4 feet heads. 

Then, as the velocity under a 16 feet head is 32.4 feet, to avoid frac¬ 
tions say 32, the gate must be drawn to only half the size, to vent the 
16 cubic feet of water per second as before (because the velocity is 
double:) then, to find the effect, 32 multiplied by 32 is equal to 1024; 
which, multiplied by 16, the quantity, gives the effect 16384, equal the 
sum of all the 4 feet heads, which agrees with the practice and ex¬ 
perience of the best teachers. But if their effects were as their veloci¬ 
ties simply, then the effect of each 4 feet head would be, 16 multiplied 
by 16, equal to 256; which, multiplied by 4, is equal to 1024, for the 
sum of the effects of all the 4 feet heads; and 16 multiplied by 32 equal 
to 512, for the effect of the 16 feet head, which is only half of the ef¬ 
fect of the same head when divided into 4 parts; which is contrary to 
both experiment and reason. 

Again, let us suppose the body A of quantity 16, to be perfectly 
elastic, to fall 16 feet and strike F, a perfectly elastic plane, it will 
(by laws of falling bodies), strike with a velocity of 32 feet per second, 
and rise 16 feet to A again.' 

But if it fall only to B, 4 feet, it will strike with a velocity of 16 feet 
per second, and rise 4 feet to A again.. Here the effect of the 16 feet 
fall is 4 times the effect of the 4 feet fall, because the body rises 4 times 
the height. 

But if we count the effective momentum of their strokes to be as 
their velocities simply, then 16 multiplied by 32 is equal to 512, the 
momentum of the 16 feet fall; and 16 multiplied by 16 is equal to 256; 
which, multiplied by 4, is equal to 1024, for the sum of the momentums 
of the strokes of 16 feet divided into 4 equal falls; which is absurd. 
But if we count their momentums to be as the squares of their velocities, 
the effects will be equal. 

Again, it is evident that whatever impulse or force is required to 
give a body velocity, the same force or resistance will be required to 
stop it; therefore, if the impulse be as the square of the velocity pro¬ 
duced, the force or resistance will be as the squares of tie velocity 


HYDRAULICS. 


91 


cnAP. hi.] 

also. But the impulse is as the squares of the velocity produced, which 
is evident from this consideration : Suppose we place a light body at 
the gate B, of 4 feet head, and pressed with 4 feet of water; when the 
gate is drawn, it will fly otf with the velocity of 16 feet per second; 
and if we increase the head to 16 feet, it will fly off with 32 feet per 
second. Then, as the square of 16 equal to 256 is to the square of 32 
equal to 1024, so is 4 to 16. Q. E. I). 


ARTICLE 47. 


# 

THE SEVENTH LAW IS IN ACCORDANCE WITH PRACTICE. 


Let us compare this 7th law with the theory of undershot mills, 
established Art. 41, where it is shown that the power is to the effect as 
3 to 1. By the 7th law, the quantity shown by the scale, Plate II., to 
be 32.4 multiplied by 1049.76, the square of the velocity, which is 
equal to 3401.2124, the effect of the 16 feet head; then, for the effect 
of a 4 feet head, with equal apertures, quantity by scale 16.2, multi¬ 
plied by 262.44, the velocity squared, is equal to 425.1528; the effect 
of a 4 feet head. Here the ratio of the effect is as 8 to 1. 

Then, by the theory, which shows that an undershot wheel will raise 
l-3d of the water that turns it, to the whole height from which it de¬ 
scended, the l-3d of 32.4, the quantity, being equal to 10.8, multiplied 
by 16, perpendicular ascent, which is equal to 172.8, effect of a 16 feet 
head: and l-3d of 16.2 quantity, which is equal to 5.4, multiplied by 
4, perpendicular ascent is equal to 21.6, effect of a 4 feet head, by the 
theory; and here again the ratio of the effects is as 8 to 1; and, 
as 3401.2124, the effect of 16 feet head, } , - , , 

is to 425.1825, the effect of a 4 feet head, ^ aw * 
so is 172,8, the effect of 16 feet head, 
to 21.6, the effect of 4 feet head, 

The quantities being equal, their effects are as the height of their 
heads directly, as by 5th law, and as the squares of their velocities, as 
by the 7th law. Hence it appears, that the theory agrees with the 
established laws. 


by the theory. 


Application of the Laics of Motion to Undershot Wheels. 

To give a short and comprehensive detail of the ideas 
I have collected from different authors, and from the re¬ 
sult of my own reasoning on the laws of motion and of 
spouting fluids, as they apply to move undershot mills, I 
refer to fig. 44, Plate V. 

Let us suppose two large wheels, one of 12 feet, and 



92 


HYDRAULICS. 


[CIIAP. III. 

the other of 24 feet radius, the circumference of the 
largest will then be double that of the smallest: and 
let A 16, and C 16, be two penstocks of water, of 16 feet 
head each, then,— 

1. If we open a gate of 1 square foot at 4, to admit 
water from penstock A 16, to impinge on the small 
wheel at I, the water being pressed by 4 feet head, will 
move 16 feet per second (we omit fractions.) The in¬ 
stant pressure or force on that gate being four cubic feet 
of water, it will require a resistance of 4 cubic feet of 
water from the head C 16 to stop it, and hold it in 
equilibrio, (but we suppose the water cannot escape, 
unless the wheel moves, so that no force be lost by non¬ 
elasticity.) Here equal quantities of matter, with equal 
velocities, have their momentums equal. 

2. Again, suppose we open a gate of 1 square foot at 
A 16 under 16 feet head, it will strike the large wheel 
at k, with velocity 32, its instant force or pressure being 
16 cubic feet of water; it will require 16 cubic feet re¬ 
sistance, from the head C 16, to stop or balance it. In 
this case, the pressure, or instant force, is quadruple to 
the first, and so is the resistance, but the velocity only 
double. In these two cases the forces and resistances 
being equal quantities, with equal velocities, their nio- 
mentums are equal. 

3. Again, suppose the head C 16 to be raised to E, 
16 feet above 4, and a gate drawn 1-4th of a square foot, 
then the instant pressure on the float I of the small 
wheel, will be 4 cubic feet, pressing on 1-4th of a square 
foot, and will exactly balance 4 cubic feet, pressing on 
1 square foot from the head A 16; and the wheel will 
be in equilibrio, (supposing the water cannot escape 
until the wheel moves as before,) although the one has 
power of velocity 32, and the other only 16, feet per 
second; their loads at equilibrio are equal, consequently, 
their loads at a maximum velocity and charge will be 
equal, but their velocities different. 

Then, to try their effects, suppose, first, the wheel to 
move by the 4 feet head, its maximum velocity to be 
half the velocity of the water, which is 16, and its max¬ 
imum load to be half its greatest load, which is 4, by 
Waring’s theory; then the velocity 16^-2 multiplied by 


HYDRAULICS. 


93 


CHAP. III.] 

the load 4 h- 2 — 16, the effect of the 4 feet head, with 
16 cubic feet expended; because the velocity of the wa¬ 
ter is 16, and the gate 1 foot. 

Again, suppose it to move by the 16 feet head and 
gate of 1-4th of a foot; then the velocity 32-4-2 multi¬ 
plied by the load 4 -4- 2 = 32, the effect, with but 8 cubic 
feet expended, because the velocity of the water is 32, 
and the gate but 1-4 th of a foot. 

In this case the instant forces are equal, each being 
4; but the one moving a body only 1-4th as heavy as 
the other, moves with velocity 32, and produces effect 
32, while the other, moving with velocity 16, produces 
effect 16. A double velocity, with equal instant pres¬ 
sure, produces a double effect, which seems to be accord¬ 
ing to the Newtonian theory. And in this sense the 
momentums of bodies in motion are as their quantities 
multiplied into their simple velocities, and this is what 
I call the instant momentums. 

But when w r e consider that in the above case it was 
the quantity of matter j3ut in motion, or water expend¬ 
ed, that produced the effect, we find that the quantity 
16, with velocity 16, produced effect 16; while quantity 
8, with velocity 32, produced effect 32. Here the ef¬ 
fects are as their quantities multiplied into the squares 
of their velocities, and this I call the effective momen¬ 
tums. 

Again, if the quantity expended under each head 
had been equal, their effects would have been 16 and 
64, which is as the squares of their velocities, 16 and 

Q9 

O Zj . 

4. Again, suppose both wheels to be on one shaft, 
and let a gate of 1-8 th of a square foot be drawn at 16 
C, to strike the wheel at K, the head being 16 feet, the 
instant pressure on the gate will be 2 cubic feet ot wa¬ 
ter, which is half of the 4 feet head with 1 foot gate, 
from A 4 striking at I; but the 16 feet head with in¬ 
stant pressure 2, acting on the great wheel, will balance 
4 feet on the small one, because the lever is of double 
length, and the wheels will be in equilibrio. Then, by 
Waring s theory, the greatest load of the 16 feet head 
being 2, its load at a maximum will be 1, and the velo¬ 
city of the water being 32, the maximum velocity of 


HYDRAULICS. 


04 


[chap. III. 


tlie wheel will be 16. Now the velocity 16 x 1 = 16, 
the effect of the 16 feet head; and gate of l-8th of a 
foot, the greatest load of the four feet head being 4, its 
maximum load 2, the velocity of the water 16, and the 
velocity of the wheel 8: now 8x2 = 16, the effect. 
Here the effects are equal, and here, again, the effects 
are as the instant pressures multiplied into their simple 
velocities; and the resistances that would instantly stop 
them must be equal thereto, in the same ratio. 

But when v r e consider that in this case the 4 feet 
head expended 16 cubic feet of water with velocity 16, 
% and produced effect 16; while the 16 feet head expend¬ 
ed only 4 cubic feet of water, with velocity 32, and pro¬ 
duced effect 16, we find that the effects are as their 
quantities, multiplied into the squares of their veloci¬ 
ties. 

And when we consider that the gate of l-8th of a 
square foot, with velocity 32, produced effects equal to 
the gate of 1 square foot, with velocity 16, it is evident 
that if w r e make the gates equal, the effects will be as 8 
to 1; that is, the effects of spouting fluids, with equal 
apertures, are as the cubes of their velocities; because, 
their instant forces are as the squares of their velocities, 
by 6th law, although the instant forces of solids are' as 
their velocities simply, and their effects as the squares 
of their velocities, a double velocity does not double 
the quantity of a solid body to strike in the same time. 


ARTICLE 48. 

THE HYDROSTATIC PARADOX. 

The pressure of fluids is as their perpendicular heights, 
without any regard to their quantity: and their pres¬ 
sure upwards is equal to their pressure downwards. In 
short, their pressure is every way equal, at any equal 
distance from their surface. 

In a vessel of cubic form, whose sides and bottom are 
equal, the pressure on each side is just half the pres¬ 
sure on the bottom; therefore, the pressure on the bot¬ 
tom and sides is equal to three times the pressure on 
the bottom. 



HYDRAULICS. 


95 


CHAP. III.] 

And, in this sense, fluids may be said to act with 
three times the force of solids. Solids act by gravity 
only, but fluids by gravity and pressure jointly. Solids 
act with a force proportional to their quantity of mat¬ 
ter, but fluids act with a pressure proportional to their 
altitude only. 

To explain the law, that the pressure of fluids is as their perpendicular heights, 
let A B C D, Plate III. fig. 22, be a vessel of water of a cubical form, with a 
small tube, as H, fixed therein; let a hole of the same size with the tube be made 
at o, and covered with a piece of pliant leather nailed thereon, so as to hold the 
water. Then fill the vessel with water by the tube H, and it will press upwards 
against the leather, and raise it in a convex form, requiring just as much weight 
to press it down, as will be equal to the weight of the water in the tube H. Or 
if we set a glass tube over the hole at o, and pour water therein, we shall find 
that the water in the tube o, must be of the same height as that in the tube H, 
before the leather will subside, even if the tube o be much larger than H; which 
shows that the pressure upwards is equal to the pressure downwards; because 
the water pressed up against the leather with the whole weight of the water 
in the tube H. Again, if we fill the vessel by the tube I, it will rise to the same 
height in II that it is in I; the pressure being the same in every part of the vessel 
as if it had been filled by H; and the pressure on the bottom of the vessel will 
be the same, whether the tube H be of the whole size of the vessel, or only one 
quarter of an inch diameter. For suppose H to be l-4th of an inch diameter, 
and the whole top of the vessel of leather, as at o, and we pour water down H, 
it will press the leather up with such force, that it will require a column of water 
of the whole size of the vessel, and height of H, to cause the leather to subside. 
Q. E. D. 


ARTICLE 49. 


PRACTICAL RESULTS OF THIS EQUAL PRESSURE. 

And again, suppose we make two holes in the vessel, one close to the bottom, 
and the other in the bottom, both of one size, the water will issue with equal 
velocity out of each; this may be proved by holding equal vessels under each, 
which will be filled in equal time; this shows that the pressure on the sides and 
bottom is equal under equal distances from the surface. And this velocity will 
be the same whether the tube be filled by pipe I, or H, or by a tube the whole 
size of the vessels, provided the perpendicular height be equal in all cases. 

From what has been said, it appears that it makes no difference in the power 
of water in mill-wheels, whether it be brought on in an open lorebay and per¬ 
pendicular penstock, or down an inclining one, as I C; or under ground in a close 
trunk, in any form that may best suit the situation and circumstances, provided 
that the trunk be sufficiently large to supply the water fast enough to keep the 
head from sinking. 

This principle of the Hydrostatic Paradox has sometimes operated in undershot 
mills, by pressing up against the bottom of the buckets, thereby destroying or 
counteracting, in great part, the force of impulse. See Art. 59. 



96 


HYDRAULICS. 


[CHAP. HI. 


ARTICLE 50. 

The weight of a cubic foot of water is found by expe¬ 
rience to be 1000 ounces avoirdupois, or 62.5 lbs. On 
the principles explained in Art. 48 and 49, is founded 
the following 


THEOREM. 

The area of the base or bottom, or any part of a ves¬ 
sel, of whatever form, multiplied by the greatest perpen¬ 
dicular height of any part of the fluid, above the centre 
of the base or bottom, whatever be its position with the 
horizon, produces the pressure on the bottom of said 
vessel. 


PROBLEM I. 

« 

Given the length of the sides of the cubic vessel (fig. 
22, PI. III.) 6 feet, required the pressure on the bottom 
when full of water. 

Then 6 x 6 = 36 feet, the area, multiplied by 6, the 
altitude, = 216, the quantity or cubic feet of water 
pressing on the bottom; which multiplied by 62.5 = 
13500 lbs., the whole pressure on the bottom. 


PROBLEM II. 

Given the height of a penstock of water, 31.5 feet, 
and its dimensions at bottom 3 by 3 feet inside, required 
the pressure on three feet high of one of its sides, mea¬ 
suring from the bottom. 

Then, 3x3 = 9, the area, multiplied by 30 feet, the 
perpendicular height or head above the centre of the 3 
feet on the side =^ 270 cubic feet of watpr pressing, 
which x 62.5 = 16875 lbs., the pressure on one yard 
square, which shows what great strength is required to 
hold the water under such great heads. 


CHAP. III.] 


HYDRAULICS. 


97 


ARTICLE 51. 

RULE FOR FINDING THE VELOCITY OF SPOUTING WATER. 

It lias been found by experiment that water will 
spout from under a 4 feet head, with a velocity equal 
to 16.2 feet per second, and from under a 16 feet head 
with a velocity equal to 32.4 feet per second. 

On these experiments, and the second law of spouting 
fluids, is founded the following theorem, or general rule, 
for finding the velocity of water under any given head. 

THEOREM. 

As the square root of a 4 feet head (= 2) is to 16.2 
feet, the velocity of the water spouting under it, so is 
the square root of any other head, to the velocity of 
the water spouting under it. 

PROBLEM I. 

Given the head of water 16 feet, required the velo¬ 
city of water spouting under it. 

Then, as the square root of 4 (= 2) is to 16.2, so is 
the square root of 16 (= 4) to 32.4 the velocity of the 
water under the 16 feet head. 

PROBLEM II. 

Given a head of water of 11 feet, required a velocity 
of water spouting under it. 

Then, as 2 :16.2 : : 3.316 : 26.73 feet per second, the 
velocity required. 


ARTICLE 52. 

EFFECT OF WATER UNDER A GIVEN HEAD. 

From the 1st and 2d laws of spouting fluids, (Art. 
45,) the theory for finding the maximum charge and 
velocity of undershot wheels, (Art. 41,) and from the 
principle of non-elasticity, the following theorem is de- 

7 



98 


II Y D R A U LIC S. 


[CHAP. III. 

duced for finding the effect of any gate drawn under 
any given head upon an undershot water wheel. 


THEOREM. 

Find by the theorem, (Art. 50,) the instantaneous pres¬ 
sure of the water, which is the load at equilibrio, and 
2-3ds thereof is the maximum load, which, multiplied 
by .577 of the velocity of the water, under the given 
head, (found by the theorem, Art. 51,) produces the ef¬ 
fect. 


PROBLEM. 

Given the head 1G feet, gate 4 feet wide, .25 of a 
foot drawn, required the effect of an undershot wheel, 
per second. The measure of the effect to be the quan¬ 
tity multiplied into its distance moved (velocity,) or 
into its perpendicular ascent. 

Then, by the theorem (Art. 50) 4 x .25 = 1 square foot 
(the area of the gate) x 16 = 1G, the cubic feet pressing; 
but, for the sake of round numbers, we call each cubic 
foot 1, and although 32.4 cubic feet strike the wheel per 
second, yet, on account of non-elasticity, only 1G Cubic 
feet is the load at equilibrio, and 2-Gths.of 16 is 10.6G6, 
the maximum load. 

Then, by theorem, (Art. 51) the velocity is 32.4, .577 
of which is = 18.71, the maximum velocity of the wheel 
x 10.66, the load =;199.4, the effect. 

This agrees with Smeaton’s observations, where he 
says, (Art. 67,) “It is somewhat remarkable that though 
the velocity of the wheel in relation to the velocity of 
the water, turns out to be more than l-3d, yet the im¬ 
pulse of the water, in case of the maximum, is more than 
double of what is assigned by theory; that is, instead of 
4-9ths of the column, it is nearly equal to the whole co¬ 
lumn.'’ Hence, I conclude that non-elasticity does not 
operate so much against this application, as to reduce 
the load to be less than 2-3ds. And when we consider 
that 32.4 cubic feet of water, or a column 32.4 feet 
long, strikes the wheel, while it moves only 18.71 feet, 


99 


CHAP. III.] HYDRAULICS. 

the velocity of the wheel being to the velocity of the 
water as 577 to 1000, may not this be the reason why 
the load is just 2-3ds of the head, which brings the ef¬ 
fect to be just .38, (a little more than l-3d of the pow¬ 
er?) This I admit, because it agrees with experiment, 
although it be difficult to assign the true reason there¬ 
of. See Annotation, Art. 42. 

Therefore, .577, the velocity of the water = 18.71, 
multiplied by 2-3ds of 16, the whole column, or instan¬ 
taneous pressure, pressing on the wheel, (Art. 50,) which 
is 10.66, produces 199.4, the effect. This appears to 
be the true effect, and if so, the true theorem will be as 
follows; namely: 


THEOREM. 

Find by the theorem, Art. 50, the instantaneous pres¬ 
sure of the water, and take 2-3ds for the maximum 
load; multiply by .577 of the velocity of the water, which 
is the velocity of the wheel, and the product will be the 
effect. 

Then 16 cubic feet, the column, multiplied bj^ 2-3ds 
= 10.66, the load, which multiplied by 18.71, the velo¬ 
city of the wheel, produces 199.4, for the effect; and if 
we try different heads and different apertures, we find 
the effects to bear the ratio to each other that is agree¬ 
able to the laws of spouting fluids. 


ARTICLE 53. 

r 

WATER APPLIED ON WHEELS TO ACT ON GRAVITY. 

When fluids are applied to act on wheels to produce 
effects by their gravity, they act on very different prin¬ 
ciples from the foregoing, producing double effects to 
what they do by percussion, and then their powers are 
directly as their quantity, or weight, multiplied into 
their perpendicular descent. 



100 


HYDRAULICS. 


[CHAP. III. 


DEMONSTRATION. 

Let D B, fig. 19, Plate III., be a lever, turning on 
its centre or fulcrum A. Let the long arm, A B, repre¬ 
sent the perpendicular descent, 16 feet, the short arm, 
A D, a descent of 4 feet, and suppose water to issue from 
the trunk F, at the rate of 50 lbs. in a second, falling 
into the buckets fastened to the lever at B. Now, from 
the principles of the lever, Art. 16, it is evident that 
50 lbs. in a second, at D, will balance 200 lbs. in a se¬ 
cond, at D, issuing from the trunk G, on the short arm; 
because 50 x 16 = 800, and 4 x 200 — 800. Perhaps 
it may appear plainer, if we suppose the perpendicular 
line or diameter, F C, to represent the descent of 16 feet, 
and the diameter, G I, a descent of 4 feet. By the laws 
of the lever, Art. 16, it is shown that to multiply 50 
into its perpendicular descent 16 feet or distance moved, 
is = 200 multiplied into its perpendicular descent 4 feet, 
or distance moved; that is, 50 x 16 = 200 x 4 = 800; 
that is, their power is as their quantity multiplied into 
their perpendicular descent; or, in other words, a fall of 
4 feet will require 4 times as much water as a fall of 
16 feet to produce equal power and effects. Q. E. D. 

Upon these principles is founded the following simple 
theorem, for measuring the power of an overshot mill, 
or of a quantity of water acting upon any mill-wheel 
by its gravity. 


THEOREM. 

. *' 

Cause the water to pass along a regular canal, and 
multiply its depth in feet and parts, by its width in feet 
and parts, for the area of its section, which product 
multiply by its velocity, per second, in feet and parts, 
and the product is the cubic feet used per second, which 
multiplied by 62.5 lbs., the weight of one cubic foot, 
produces the weight of water per second that falls on 
the wheel, which multiplied by its whole perpendicular 
descent, gives a true measure of its power. 


CHAP. III.] 


HYDRAULICS. 


101 


PROBLEM I. 

Given a mill seat with 16 feet fall, width of the canal 
5.333 feet, depth 3 feet, velocity of the water passing 
along it 2.03 feet per second, required the power per 
second. 

Then, 5.333 x 3 = 15.999 feet, the area of the section 
of the stream, multiplied by 2.03 feet, the velocity, is 
equal 32.4 cubic feet, the quantity per second, multi¬ 
plied by 62.5 is equal 2025 lbs. the weight of the water 
per second, multiplied by 16, the perpendicular de¬ 
scent, is equal 32400, for the power of the seat per se¬ 
cond. 


PROBLEM II. 

. Given, the perpendicular descent 18.3 width of the 
gate 2.66 feet, height .145 of a foot, velocity of the water 
per second issuing on the wheel, 15.76 feet, required the 
power. 

Then, 2.66 x .145 = .3857 the area of the gate, x 
15.76 the velocity = 6.178 cubic feet expended per 
second, x 62.5 = 375.8 lbs. per second, x 18.3 feet per¬ 
pendicular descent = 6877 for the measure of the power 
per second; which has ground 3.75 lbs. per minute, equal 
3.75 bushels in an hour, with a five feet pair of burr 
stones. 


ARTICLE 54. 

INVESTIGATION OE THE PRINCIPLES OP OVERSHOT MILLS. 

Some have asserted, and many believed, that water 
is applied to great disadvantage on the principle of an 
overshot mill; because, say they, there are never more 
than two buckets, at once, that can be said to act fairly 
on the end of the lever, (as the arms of the wheel are 
called in these arguments.) But we must examine well 
the laws of bodies descending inclined planes, and curved 
surfaces. See Art. 11. This matter will be cleared 
up, if we consider the circumference of the wheel to 



102 


HYDRAULICS. 


[CIIAP. III. 

be the curved surface; for the fact is, that the water acts 
to the best advantage, and produces effects equal to 
what it would, in case the whole of it acted upon the very 
end of the lever, in the whole of its perpendicular de¬ 
scent. The want of a knowledge of this fact has led to 
many fatal errors in the application of water. 


DEMONSTRATION. 

Let A B C, Plate III. fig. 20, represent a water¬ 
wheel, and F II a trunk, bringing water to it from a 
16 feet head. Now suppose F G and 16 H to be two 
penstocks under equal heads, down which the water de¬ 
scends, to act on the wheel at C on the principle of an 
undershot, on opposite sides of the float C with equal 
apertures; it will be evident from the principles of 
hydrostatics, shown by the paradox, (Art. 48, and the 
first law of spouting fluids, Art. 45,) that the impulse 
and pressure will be equal from each penstock respec¬ 
tively. Although the one be an inclined plane, and the 
other a perpendicular, their forces are equal, because 
their perpendicular heights are so; (Art. 48,) therefore, 
the wheel will remain at rest, because each side of the 
lloat is pressed on by a column of water of equal size and 
height, as represented by the lines on each side of the 
float. Then, suppose we shut the penstock F G, and 
let the Avater down the circular one r x, which is close 
to the point of the buckets; this makes it obvious, from 
the same principles, that the wheel will be held in 
equilibrio, if the columns of each side be equal. For, 
although the column in the circular penstock is longer 
than the perpendicular one, yet, because part of its 
weight presses on the lower side of the penstock, its 
pressure on the float is only equal to its perpendicular 
height. 

Then, again, suppose the column of water in the circu¬ 
lar penstock to be instantly thrown into the buckets, it 
is evident that the wheel will be still held in equilibrio, 
and each bucket will then bear a proportional part of the 
column that the bucket C bore before; and that part of 


HYDRAULICS. 


103 


CHAP. III.] 

the weight of the circular column, which rested on the 
under side of the circular penstock, is now on the gud¬ 
geons of the wheel. This shows that the effect of a 
stream, applied on an overshot wheel, is equal to the 
effect of the same stream, applied on the end of the 
lever, in its whole perpendicular descent, as in fig. 21, 
where the water is shot into the buckets fastened to a 
strap or chain revolving over two wheels; and here the 
whole force of the gravity of the column acts on the 
very end of the lever in the whole of the descent. Al¬ 
though the length of the. column in action, in this case, 
is only 16 feet, whereas, on a 16 feet wheel, the length 
of the column in action is 25.15, yet their powers are 
equal. 

Again, if we divide the half circle into three arches, 
Ab, be, eC, the centre of gravity of the upper and lower 
arches will fall near the point a, 3.9 feet from the cen¬ 
tre of motion, and the centre of gravity of the middle 
arch, near the point o, 7.6 feet from the centre of mo¬ 
tion. Now, each of these arches is 8.38 feet, and 8.38 
x 2 x 3.9 = 65.36, and 8.38 x 7.6 feet = 63.07, which 
two products added — 128.43, for the momentum of the 
circular column, by the laws of the lever, and for the 
perpendicular column 16 x 8 the radius of the wheel 
— 128, for the momentum; by which it appears that 
if we could determine the exact jioints on which the 
arches act, the momenturns would be equal; all which 
shows that the power of water on overshot wheels is 
equal to the whole power it can any way produce, 
through the whole of its perpendicular descent, except 
what may be lost to obtain velocity (Art. 41,) overcome 
friction, or by spilling a part of the water before it gets 
to the bottom of the wheel. Q. E. D. 

I may add that I have made the following experi¬ 
ment, namely: I fixed a truly circular wheel on nice pi¬ 
vots, to avoid friction, and took a cylindrical rod of thick 
wire, cutting one piece exactly the length of half the 
circumference of the wheel, and fastening it to one side, 
close to the rim of the wheel its whole length, as at G x 
r a. I then took another piece of the same wire, of a 
length equal to the diameter of the wheel, and hung it 


'104 


hydraulics. 


[chap. III. 

on the opposite side, on the end of the lever or arm, as 
at B, and the wheel was in equilibrio. Q. E. D. 


ARTICLE 55. 

ON THE FRICTION OF THE APERTURES OF SPOUTING FLUIDS. 

The doctrine of this species of friction appears to be 
as follows:— 

1. The ratio of the friction of round apertures is as 
their diameters, nearly; while the quantity expended 
is as the squares of their diameters. 

2. The friction of an aperture of any regular or irre¬ 
gular figure, is as the length of the sum of the circum¬ 
scribing lines, nearly; the quantities being as the areas 
of the aperture.* Therefore, 

3. The less the head or pressure, and the larger the 
aperture, the less the ratio of the friction; therefore, 

4. This friction need not be much regarded in the 
large openings or apertures of undershot mills, where the 
gates are from 2 to 15 inches in their shortest sides; but 
it very sensibly affects the small apertures of high over¬ 
shot or undershot mills, with great heads, where their 
shortest sides are from T A-tlis of an inch to two inches.f 

* This will plainly appear, if we consider that the friction does sensibly re¬ 
tard the velocity of the fluid to a certain distance; say half an inch from the side 
or edge of the aperture, towards its centre; and we may reasonably conclude that 
this distance will be nearly the same in a 2 and 12 inch aperture; so that in the 
2 inch aperture, a ring on the ontside, half an inch wide, is sensibly retarded, 
which is about 3-4ths of the whole: while, in the 12 inch aperture, there is a ring 
on the outside half an inch wide, retarded about one sixth of its whole area. 

f This seems to be proved by Smeaton, in his experiments ; (see table Art.G7 ;) 
where, when the head was 33 inches, the sluice small, drawn only to the 1st hole, 
the velocity of the water was only such as is assigned by theory to a head of 
15.85 inches, which he calls virtual head. But when the sluice was larger, 
drawn to the 6th hole, and head 6 inches, the virtual head was 5.33 inches. But 
seeing there is no theorem, yet discovered, by which we can truly determine 
the quantity or effect of the friction, according to the size of the aperture, and 
height of the head; we cannot, therefore, by the established laws of hydrostatics, 
determine exactly the velocity or quantity expended through any small aperture; 
which renders the theory in these cases but little better than conjecture. 



cnAP. hi.] 


HYDRAULICS. 


105 


ARTICLE 56. 

OF THE PRESSURE OF THE AIR ON FLUIDS. 

Under certain circumstances, the rise of water is 
caused by the pressure of the air on the surface of its 
reservoir or source; and this pressure is equal to that 
of a head of water of about 33| feet perpendicular height; 
under which pressure or height of head, the velocity of 
spouting water is 46.73 feet per second. 

If, therefore, we could by any means take off the pres¬ 
sure of the atmosphere, from any one part of the surface 
of a fluid, that part would spout up with a velocity of 
46.73 feet per second, and rise to the height of 331 feet 
nearly. 

All syphons, or cranes, and all pumps for raising wa¬ 
ter by suction, as it is called, act on this principle.—Let 
fig. 23, PI. III. represent a cask of water, with a syphon 
therein, to extend 331 feet above the surface of the wa¬ 
ter in the cask. Now, if the bung be made perfectly 
air-tight round the syphon, so that no air can get into 
the cask, and the cask be full, and if all the air be then 
drawn out of the syphon, the fluid will not rise in the 
syphon, because the air cannot get to it to press it up; 
but take out the plug P, and let the air into the cask, 
to press on the surface of the water, and it will spout up 
the short leg of the syphon B A, with the same force 
and velocity as if it had been pressed with a head of 
water 331 feet high, and will run into the long leg and 
fill it. If we then turn the cock c, and let the water 
run out, its weight in the long leg w T ill overbalance the 
weight in the short one, drawing the water out of the 
cask until it sinks so low that the leg B A will be 331 
feet high, above the surface of the water in the cask; 
it will then stop, because the weight of water in the legs, 
in which it rises, will be equal to the weight of a column 
of the air of equal size, and of the whole height of the 
atmosphere. The water will not run out of the leg A 
C, but will stand 331 feet above its mouth, because the 
air will press up the mouth C, with a force that will 


106 


HYDRAULICS. 


[cnAP. III. 

balance 331 feet of water in tlie leg C A. This will be 
the case, let the upper part of the leg be of any size 
whatever; and there will be a vacuum at the upper 
end of the syphon. 

It must not, however, be supposed that if the mouth 
C be left open, after the water has ceased running, that 
the portion of it which is in the leg A C, will remain 
there, as air will be gradually admitted, and will press 
upon the upper end of the column A 13, which will then 
descend into both legs. 


ARTICLE 57. 

OF PUMPS. 

Let fig. 24, PI. III. represent a pump of the common 
kind used for drawing water out of wells. The movable 
valve or bucket A, is cased with leather, which springs 
outwards, and fits the tube so nicely that neither air 
nor water can pass freely by it. When the lever L is 
worked, the valve A opens as it descends, letting the 
air or water pass through it. As it ascends again, the 
valve shuts, the water which is above the bucket A is 
raised, and there would be a vacuum between the valves, 
but the weight of the air presses on the surface of the 
water in the well, at W, forcing it up through the valve 
B, to fill the space between the buckets; and as the 
valve A descends, B shuts, and prevents the water from 
descending again. But if the upper valve A be set more 
than 331 feet above the surface of the water in the well, 
the pump cannot be made to draw, because the pressure 
of the atmosphere will not cause the water to rise more 
than 33£ feet. Although in theory the water would 
rise to the height stated, yet in point of fact the distance 
between the valve in the piston and the surface of the 
water in the well, ought never to exceed 24 or 25 feet, 
or, from the imperfection of workmanship, and other 
causes, the pump will lose water , and will cease to act. 



CIIAF. III.] 


HYDRAULICS. 


107 


A TABLE FOR PUMP MAKERS. 


Height of the 
pump, in feet, 
above the sur¬ 
face of the 
well. 

Diameter of 
the bore. 

=• ^5 

aT .-.’Td 

CD a y 

Water discharged 
in a minute, in 
wine measure. 

O Tl 

£L S' 

rn y: 

• • 

10 

6 

93 

81 

6 

15 

5 

66 

54 

4 

20 

4 

90 

40 

7 

25 

4 

38 

32 

6 

30 

4 

00 

27 

2 

35 

3 

70 

23 

3 

40 

3 

46 

20 

3 

45 

3 

27 

18 

1 

50 

3 

10 

16 

3 

55 

2 

95 

14 

7 

60 

2 

84 

13 

5 

65 

2 

72 

12 

4 

70 

2 

62 

11 

5 

75 

o 

53 

10 

i 

80 

2 

45 

10 

2 

85 

2 

38 

9 

5 

90 

2 

31 

9 

1 

95 

2 

25 

8 

5 

100 

2 

18 

8 

1 1 


The preceding table is extracted from Ferguson’s Lectures, and its use is 
pointed out by him in the subjoined quotation : before giving which, however, it 
will be proper to remark, that it is a common practice to make the bore in the 
lower part of the pump-tree smaller than the chamber, under the erroneous sup¬ 
position that there will be a less weight of water to lift in 1 his than in a larger 
bore. The consequence of this is, that the water has to rush with greater ve¬ 
locity in order to fill the capacity of the chamber, by which much friction is 
caused and much power wasted. 

“All pumps should be so constructed as to work with equal ease in raising 
the water to any given height above the surface of the well: and this may be 
done by observing a due proportion between the diameter of that part of the 
pump-bore in which the piston or bucket works, and the height to which the 
water must be raised. 

“For this purpose I have calculated the above table; in which the handle of 
the pump is supposed to be a lever, increasing the power five times: that is, the 
distance or length of that part of the handle that lies between the pin on which 
it moves, and the top of the pump rod to which it is fixed, to be only one-fifth part 
of the length of the handle, from the said pin to the part where the man "who 
works the pump applies his force or power. 

<{ In the first column of the table, find the height at which the pump must dis¬ 
charge the water above the surface of the well: then in the second column you 
have the diameter of that part of the bore in which the piston or bucket works, in 
inches and hundredth parts of an inch; in the third column is the quantity of 
water (in wine measure) that a man of common strength can raise in a minute.— 
And by constructing according to this method, pumps of all heights may be 
wrought by a man of ordinary strength, so as to be able to hold out for an hour.” 

















108 


HYDRAULICS. 


[CHAP. III. 


ARTICLE 58. 

OF CONVEYING WATER UNDER VALLEYS AND OVER HILLS. 

Water, by its own pressure, and the pressure of the 
atmosphere, may be conveyed under valleys and over 
hills, to supply a family, a mill or a town. In fig. 20, PI. 
III. F II is a canal for conveying water to a mill-wheel: 
now let us suppose F G 16 H to be a tight tube or trunk, 
—the water being let in at F, it will descend from F to 
G, and its pressure at F, will cause it to rise to II, 
which shows how it may be conveyed under a valley; 
and it may be conveyed over a hill by a tube, acting on 
the principle of the syphon. (Art. 56.) But some who 
have had occasion to convey water, under any obstacle, 
for the convenience of a mill, have gone into the fol¬ 
lowing expensive error; they have made the tube at G 
16, smaller than they would if it had been on a level; 
because, say they, a greater quantity will pass through 
a tube, pressed by the head G F, than on a level; but 
it should be considered that the head G F, is balanced by 
the head II 16, and the velocity through the tube G 16, 
will be such only, as a head equal to the difference' be¬ 
tween the perpendicular height of G F, and II16, would 
give it (see Art. 41, fig. 19;) therefore, it should be as 
large at G 16, as if on a level. 


ARTICLE 59. 

OF THE DIFFERENCE IN TIIE FORCE OF INDEFINITE AND DEFINITE 
QUANTITIES OF WATER STRIKING A WHEEL. 

DEFINITIONS. 

1. By an indefinite quantity of water we here mean 
a river, or quantity much larger than the float of the 
wheel, so that, when it strikes the float, it has liberty 
to move or escape from it in every lateral direction. 

2. By a definite quantity of water we mean a quantity 



HYDRAULICS. 


109 


CHAP. III.] 

passing through a given aperture, along a sliute, to 
strike a wheel; but as it strikes the float, it has liberty 
to escape in every lateral direction. 

3. By a perfectly definite quantity we mean a quan¬ 
tity passing along a close tube, so confined that when 
it strikes the float, it has not liberty to escape in any 
lateral direction. 

First, When a float of a wheel is struck by an indefi¬ 
nite quantity, the float is struck by a column of water, 
the section of which is equal to the area of the float; and 
as this column is confined on every side by the surround¬ 
ing water which has equal motion, it cannot escape 
sideways without some resistance; more of its force, there¬ 
fore, is communicated to the float, than would be, if it 
had free liberty to escape in every direction. 

Secondly, The float being struck by a definite quan¬ 
tity, with liberty to escape freely in every lateral'direc¬ 
tion, it acts as the most perfectly non-elastic body; there¬ 
fore (by Art. 9) it communicates only a part of its force, 
the other part being spent in the lateral direction. 
Hence it appears, that in the application of water to 
act by impulse, we should draw the gate as near as 
possible to the float-board, and confine it as much as 
possible from escaping sideways as it strikes the float; 
but taking care, at the same time, that we do not bring 
the principle of the Hydrostatic Paradox into action. 
(Art. 48.) 

What proportion of the force of the water is spent in 
a lateral direction is not determined. 

4. A perfectly definite quantity striking a plane, 
communicates its whole force, because no part can escape 
sideways; and is equal in power to an elastic body, 
or to the weight of the water on an overshot wheel, in 
its whole perpendicular descent. But this application 
of water to wheels in this way, has hitherto proved im¬ 
practicable; for whenever we attempt to confine the 
water totally from escaping sideways, we bring the 
principle of the hydrostatic paradox into action, which 
defeats the scheme. 

To make this plain, let fig. 25, PI. III. be a water¬ 
wheel, and, first, let us suppose the water to be brought 


110 


HYDRAULICS. 


[CHAP. III. 

to it, by the penstock 4.1G, to act by impulse on the float 
board, having liberty to escape every way as it strikes; 
then, by Art. 9, it will communicate but half its force. 
But if it be. confined both at the sides and bottom, and 
can escape only upwards, to which the gravity will 
make some opposition, it will communicate more than 
half its force, and will not react back against the float 
C; but if we put soaling to the wheel, to prevent the 
water from escaping upwards, then the space between 
the floats will be filled as soon as the wheel begins to 
be retarded, and the paradoxical principle, Art. 48, is 
brought fully into action; namely: the pressure of water 
is every way equal; and it will press backwards against 
the bottom of the float C, with a force equal to its pres¬ 
sure on the top of the float b, and the wheel will imme¬ 
diately stop, and be held in equilibrio, and will not 
start again, although all resistance be removed. There 
are many mills, where this principle is, in part, brought 
into action, which very much lessens their power. 


ARTICLE 60. 

OF THE MOTION OF BREAST AND PITCH-BACK WHEELS. 

Many have been of opinion, that when water is put to 
act on a low breast wheel, as at a, (PI. 3, fig. 25,) with 
12 feet head, that then the four feet fall, below the point 
of impact a, is totally lost, because, say they, the impulse 
of the 12 feet head will require the wheel to move with 
such velocity to suit the motion of the water, as to move 
before the action of gravity; therefore, the water cannot 
act after the stroke; but if they will consider well the 
principles of gravity acting on falling bodies, (Art. 10,) 
they will find that if the velocity of a falling body be 
ever so great, the action of gravity to cause it to move 
faster is still the same; so that, although an overshot wheel 
may move before the power of the gravity of the water 
thereon, yet no impulse downwards can give awheel such 



IIYD R AULICS. 


CHAP. III.] 


Ill 


velocity, as that the gravity of the water acting thereon 
can be thereby lessened.* 

Hence, it appears that when a greater head is used 
than that which is necessary to shoot the water fairly 
into the wheel, the impulse should be directed a little 
downward, as at D, (which is called pitch-back,) and it 
should have a circular sheeting, to prevent the water 
from leaving the wheel; because if it be shot horizontally 
on the top of the wheel, the impulse in that case will not 
give the water any greater velocity downwards, and, in 
this case, the fall would be lost, if the head were very 
great; and if the wheel moved to suit the velocity of the 
impulse, the water would be thrown out of the buckets 
by the centrifugal force; and if we attempt to retard 
the wheel so as to retain the water, the mill would be 
so ticklish and unsteady, that it would be almost im¬ 
possible to attend it. 

Hence may appear the reason why breast-wheels ge¬ 
nerally run quicker than overshots, although the fall, 
after the water strikes, be not so great. 

1. There is generally more head allowed to breast- 
wheels than to overshots; and the wheel will incline 
to move with nearly 2-3ds the velocity of the water 
spouting from under the head. Art. 41. 

2. If the water were permitted to hill freely after it 
issues from the gate it would be accelerated by the fall, 
so that its velocity at the lowest point would be equal to 
its velocity had it spouted from under a head equal to 
its whole perpendicular descent. This accelerated ve¬ 
locity of the water tends to accelerate the wheel; hence, 
to find the velocity of a breast-wheel, where the water 
strikes it in the direction of a tangent, as in fig. 31, 32, 
I deduce the following: 


* If gravity could be either decreased by velocity downwards or increased by 
velocity upwards, then a vertical wheel without friction, either of gudgeons or 
air, would require a great force to continue its motion: because its velocity 
would decrease the gravity of its descending and increase that of its ascending 
side, which would immediately stop it; whereas, it is known that it requires no 
pow T er to continue its motion, but that which is necessary to overcome the 
friction of the gudgeons, &c. 


112 


HYDRAULICS. 


[CHAP. III. 


THEOREM. 

1. Find the difference of the velocity of the water 
under the head allowed to the wheel, above the point 
of impact, and the velocity of a body having fallen the 
whole perpendicular descent of the water. Call this 
difference the acceleration by the fall: Then say, As 
the velocity a body would acquire in falling through the 
diameter of any overshot wheel, is to the proper velocity 
of that wheel by the scale, (Art. 43,) so is the accelera¬ 
tion by the fall of the water before it strikes the wheel, 
to the acceleration of the wheel by its fall, after it 
strikes. 

2. Find the velocity of the water issuing on the 
wheel; take, .577 of said velocity, to which add the ac¬ 
celerated velocity, and that sum will be the velocity of 
the breast-wheel. 

This rule will hold nearly true, when the head is con¬ 
siderably greater than is assigned by the scale, (Art. 43;) 
but as the head approaches that assigned by the scale, 
this rule will give the motion too quick. 


EXAMPLE. 

» 

Given a high breast wheel, fig. 25, where the water 
is shot on at D, the point of impact—6 feet head and 
10 feet fall—required the motion of the circumference 
of the wheel, working to the best advantage, or maxi¬ 
mum effect. 

The velocity of a falling body having 16 
feet fall, the whole descent, 

Then the velocity of the water issuing 
on the wheel, 6 feet head, 


32.4 feet. 
lg ]> 19.34 do. 


Difference, - - . - - - 13,06 do. 

Then as the velocity under a 16 feet fall (32.4 feet,) 
is to the velocity of an overshot wheel = 8.76 feet, so is 
13.06 feet to the 16 feet diameter velocity accelerated, 
which is equal 3.5 feet, to which add, .577 of 19.34 feet, 
(being 11.15 feet:) and this amounts to 14.65 feet per se¬ 
cond, the velocity of the breast-wheel. 



C1IAP. III.] 


II YDRAULIC S. 


113 


ARTICLE 61. 

RULE FOR CALCULATING THE POWER OF ANY MILL-SEAT. 

The only loss of power sustained by using too much 
head, in the application of water to turn a mill-wheel, 
is from the head producing only half its power. There¬ 
fore, in calculating the power of 16 cubic feet per se¬ 
cond on the different applications of fig. 25, PI. III., we 
must add half the head to the whole fall, and count that 
sum the virtual perpendicular descent. Then, by the 
theorem in Art. 53, multiply the weight of the water 
per second by its perpendicular descent, and you have 
the true measure of its power. 

But to simplify the rule, let us call each cubic foot 1, 
and the rule will then be—Multiply the cubic feet ex¬ 
pended per second, by its virtual perpendicular descent 
in feet, and the product will be a true measure of the 
power per second. This measure must have a name, 
which I call Cubocli; that is, one cubic foot of water, 
multiplied by one foot descent, is one cuboch, or the 
unit of power. 


EXAMPLES. 

1. Given 16 cubic feet of water per second, to be ap¬ 
plied by percussion alone, under 16 feet head, required 
the power per second. 

Then half 16 = 8x16 = 128 cubochs for the mea¬ 
sure of the power per second. 

2. Given 16 cubic feet per second, to be applied to 
a half breast of 4 feet fall and 12 feet head, required 
the power. 

Then, half 12 = 6+ 4 = 10x16=160 cubochs for 
the power. 

3. Given 16 cubic feet per second, to be applied to a 
pitch-back or liigh-breast—fall 10, head 6 feet, required 
the power. 

8 


114 


HYDRAULICS. [CHAP. III. 


Then, half 6 = 3 + 10 =13 x 10 = 208 cubochs, for 
the power per second. 

4. Given 16 cubic feet of water per second to be ap¬ 
plied as an overshot—head 4, fall 12 feet, required the 
power. 

Then, half 4 = 2 +12 = 14 x 16 = 224 cuboclis, for 
the power. 

The powers of equal quantities of water amounting 
to 16 cubic feet per second, the total perpendicular de¬ 
scents being equal, stand thus by the different modes of 
application:— 

f 16 feet head,* 


The undershot, 4 0 fall, 

(128 cuboclis of power. 

| 12 feet head, 

The half breast, -< 4 feet fall, 

(160 cuboclis of power, 
f 6 feet head, 

The high-breast, -MO feet fall, 

( 208 cuboclis of power. 

14 feet head, 

The overshot, -<12 feet fall, 

I 224 cuboclis of power. 

12.5 feet head, 

Ditto, -<31.5 feet fall, 

^263 cuboclis of power. 

The last being the head necessary to shoot the water 
fairly into the buckets, may be said to be the best ap¬ 
plication. See Art. 43. 

On these simple rules, and the rule laid down in Art. 
43, for proportioning the head and fall, I have calcu- 


* Water, by percussion, spends its force on the wheel in the following time, 
which is in proportion to the distance apart of the float-hoards and the difference 
of the velocity of the water and the wheel. 

If the water runs with double the velocity of the wheel, it will spend all its 
force on the floats while the water runs to the distance of two float-boards, and 
while the wheel runs to the distance of one; therefore, the water need not be 
kept to act on the wheel farther from the point of impact than the distance of 
about two float-boards. 

But if the wheel run with tw ? o-thirds of the velocity of the water, then, while 
the w'heel runs the distance of two floats, and while the water would have run 
the distance of three floats, it spends all its force; therefore the w r ater need be 
kept to act on the wheel the distance of three floats only past the point of im¬ 
pact. 

If it be continued in action much longer, it will fall back, and re-act against 
the following bucket, and retard the wheel. 


CHAP. III.] HYDRAULICS. 115 

lated the following table or scale of the different quan¬ 
tities of water expended per second, with different per¬ 
pendicular descents, to produce a certain power, in or¬ 
der to present at one view the ratio of increase or de¬ 
crease of quantity, as the perpendicular descent in¬ 
creases or decreases. 

A TABLE, 

Showing the quantity of water required, with different falls, to produce, by its 
gravity, 112 cubochs of power, which will drive a five feet stone about 07 
revolutions in a minute, grinding about five bushels of wheat in an hour. 


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5.6 

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18.6 

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16 

22 

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4.87 

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24 

4.66 

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25 

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28 

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3.86 

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7.46 

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3.73 


ARTICLE 62. 

THEORY AND PRACTICE COMPARED. 

I will here give a table of 18 mills in actual practice, 
out of about 50 of which I have taken an account, in or¬ 
der to compare theory with practice, and in order to as- 

















lie 


HYDRAULICS. 


[CHAP. III. 

certain the power required on each superficial foot of 
the acting parts of the stone. But I must premise the 
following 


THEOREMS. 

1. To find the circumference of any circle, as of a 
mill-stone, by the diameter, or the diameter by the cir¬ 
cumference; say, 

As 7 is to 22, so is the diameter of the stone to the 
circumference; that is, multiply the diameter by 22, and 
divide the product by 7, for the circumference; or mul¬ 
tiply the circumference by 7, and divide the product by 
22, for the diameter. 

2. To find the area of a circle by the diameter: As 
1, squared, is to .7854, so is the square of the diameter 
to the area; that is, multiply the square of the diame¬ 
ter by .7854, and, in a mill-stone, deduct one foot for 
the eye, and you have the area of the stone. 

3. To find the quantity of surface passed by a mill¬ 
stone : the area, squared, multiplied by the revolutions 
of the stone, gives the number of superficial feet passed 
in a given time. 


OBSERVATIONS ON THE FOLLOWING TABLE OF EXPERIMENTS. 

I have asserted in Art. 44, that the head above the 
gate of a wheel, on which the water acts by its gravity, 
should be such, as to cause the water to issue on the 
wheel, with a velocity to that of the wheel, as 3 to 2. 
Compare this with the following table of experiments. 

1. Exp. Overshot. Velocity of the water 12.9 feet 
per second, velocity of the wheel 8.2 feet per second, 
which is a little less than 2-3ds of the velocity of the 
water. This wheel received the water well. It is at 
Stanton, in Delaware state. 

2. Overshot. Velocity of the water 11.17 feet per 
second, 2-3ds of which is 7.44 feet; velocity of the wheel 
8.5 feet per second. This received the water pretty 
well. It is at the above-mentioned place. 


HYDRAULICS. 


117 


CHAP. III.] 

3. Overshot. Velocity of the water 12.16 feet per 
second, velocity of the wheel 10.2; throws out great part 
of the water by the back of the buckets, which strikes 
it, and makes a thumping noise. It is allowed to run 
too fast; revolves faster than my theory directs. It is 
at Brandywine, in Delaware state. 

4. Overshot. Velocity of the water 14.4 feet per se¬ 
cond, velocity of the wheel 9.3 feet, a little less than 
2-3ds of the velocity of the water. It receives the wa¬ 
ter very well; has a little more head than assigned by 
theory, and runs a little faster; it is a very good mill, 
situated at Brandywine, in the state of Delaware. 

6. Undershot. Velocity of the wheel, loaded, 16, 
and when empt}^ 24 revolutions per minute, which con¬ 
firms the theory of motion for undershot wheels. See 
Art. 42. 

7. Overshot. Velocity of the water 15.79 feet, velo¬ 
city of the wheel 7.8 feet; less than 2-3ds of the velocity 
of the water; motion slower and head more than as¬ 
signed by theory. The miller said the wheel ran too 
slowly, that he would have it altered; and that it worked 
best when the head was considerably sunk. This mill 
is at Bush, Hartford county, Maryland. 

8. Overshot. Velocity of the water, 14.96 feet per 
second; velocity of the wheel 8.8 feet, less than 2-3ds, 
very near the velocity assigned by the theory; but the 
head is greater, and the wheel runs best, when the head 
is sunk a little; is counted the best mill, and is at the 
same place with the last mentioned. 

9. 10, 11,12. Undershot open wheels. Velocity of 
the wheels when loaded 20 and 40, and when empty 
28 and 56 revolutions per minute, which is faster than 
my theory for the motion of undershot mills. Ellicott’s 
mills, near Baltimore, Maryland, serve to confirm the 
theory. 

14. Overshot. Velocity of the water 16.2 feet, velo¬ 
city of the wheel 9.1 feet, less than 2-3ds of the water, 
revolutions of the stone 144 per minute, the head nearly 
the same as by theory, the velocity of the wheel less, 
stone more. This shows the mill to be geared too high. 


118 


HYDRAULICS. 


[CHAP. III. 

The wheel receives the water well, and the mill is 
counted a very good one, situated at Alexandria, in 
Virginia. 

15. Undershot. Velocity of the water 24.3 feet per 
second, velocity of the wheel 16.67 feet, more than 2-3ds 
the velocity of the water. Three of these mills are in 
one house, at Richmond, Virginia:—they confirm the 
theory of undershots, being very good mills. 

16. Undershot. Velocity of the water 25.63 feet per 
second, velocity of the wheel 19.05 feet, being more than 
2-3ds. Three of these mills are in one house, at Peters¬ 
burg, in Virginia:—they are very good mills, and con¬ 
firm the theory. See Art. 43. 

18. Overshot wheel. Velocity of the water 11.4 feet 
per second, velocity of the wheel 10.96 feet, nearly as 
fast as the water. The backs of the buckets strike the 
water, and drive a great part over; and as the motion 
of the stone is about right, and the motion of the wheel 
faster than assigned by the theory, it shows the mill to 
be too low geared, all which confirm the theory. See 
Art. 43. 

In the following table I have counted the diameter of 
the mean circle to be 2-3ds of the diameter of the great 
circle of the stone, which is not strictly true. The mean 
circle, to contain half the area of any given circle, must 
be .707 parts of the diameter of the said circle, differing 
but little from .7, and somewhat exceeding 2-3ds. 

Hence the following theorem for finding the mean cir¬ 
cle of any stone. 

THEOREM. 

» 

Multiply the diameter of the stone by .707, and the 
product is the diameter of the mean circle. 


EXAMPLE. 

Given, the diameter of the stone, 5 feet; required a 
mean circle that shall contain half its area. 

Then 5 x .707 = 3.535 feet, the diameter of the 
mean circle. 


CHAP. III.] 


HYDRAULICS. 


119 


ARTICLE 63. 

FARTHER OBSERVATIONS ON THE FOLLOWING TABLE. 

1. The mean power used to turn the 5 feet stones in 
the experiments (No. 1, 7, 14, 17,) is 87.5 cubochs of 
the measure established, Art. 61, and the mean velocity 
is 104 revolutions of the stones in a minute, the velocity 
of the mean circle being 18.37 feet per second, and their 
mean quantity ground is 3.8 lbs. per minute, which is 
3.8 bushels per hour, and the mean power used to each 
foot of the area of the stone is 4.69 of the measure 
aforesaid, effected by 36582 superficial feet, passing each 
other in a minute. Hence we may conclude, 

1. That 87.5 cubochs of power per second will turn 
a 5 feet stone 104 revolutions in a minute, and grind 
3.8 bushels in an hour. 

2. That 4.69 cubochs of power are required to every 
superficial foot of a mill-stone, when its mean circle 
moves with a velocity of 18.37 feet per second. Or, 

3. That for every 36582 feet of the face of stones 
that pass each other, we may expect 3.8 lbs. will be 
ground, when the stones, grain, &c., are in the same 
state and condition as they were in the above experi¬ 
ments. 


120 


HYDRAULICS 


[CHAP. Ill 


A TABLE OF EXPERIMENTS ON EIGHTEEN 


MILLS IN PRACTICE. 


Quantity ground per 
minute in lbs. or per 
hour in bushels. 


3.5 

2.5 

3.75 

4.5 

3.5 

Superficial feet passed 
in a minute. 


34594 

21514 

36435 

35741 

108091 

36435 

36435 

95264 

49678 

39558 

74850 

35741 

Velocity of the mean 
circle. 

feet. 

17.3 

18.5 

16.97 

18.6 

18 32 

17.97 

17.84 

1832 

18.32 

16.92 

16.89 

19.89 

20.75 

199 

17.97 

Power required to each 
foot of face. 


tj. *o 

rH CO C3 OS <0 rH 

-t iC . . . to 

Area of the stones. 

£ 

3 

03 

18.63 
13 13 

18.63 

18.63 

38.48 

• 

! 

18.63 

36.63 

23.76 

18.63 

28.38 

18.63 

Diameter of stones in 
feet and inches. 

ft.in. j 

O © 

co or oo to to n i-h i-< t ® 'T ■*roo 

■<* -r rr •'f inwt- io -r 1 so <ouoioio«o*OTj<'r 

Revolutions of the 
stones per minutes. 


oo 

oi ^ Ci (N ^ X CO DO CO CO DO DO do rHOO^COiOCO^CD 

Q (M (J» Ct C O rrf C ch O O O hOOHHCJOOJr 

HHHHrlH r—' rH rH rH rH rH H H H n 

Rounds in trundles. | ISSSSSSS SS8 S JS S SSSSSSSS 

Cogs in the counter 
cog-wheels. 


Tf oo 'f tj* Tf Tf oo -f rvr -voooo 

m -*r . . . ■*j , -3<io..TrTTr 

Rounds in the vval- 
lowers. 


t- C) ^ H H n 0)01 ifOrfkO co co © 

d CM CM (M (M d (M CM (M # <M d d CM 01 04 

Number of cogs in the 
master-wheel. 


00 00 CM CD CM GCtMH <d rp d O CO © rf CD d 

oo oo cd t-oo rr oo ^ a oc^cdP' 

Velocity of circumfe¬ 
rence per second. 


8.2 

8.5 

10.2 

9.3 

9.8 

loaded 

unloaded 

7.8 

8.8 

loaded 

unloaded 

loaded 

unloaded 

loaded 

unloaded 

loaded 

unloaded 

7.8 

9.1 
16.67 
19.05 

9.2 
10.96 

Number of revolutions 
per minute. 


inn ^ r-A-oio —— -r—- >-'i 

co a s co •<?» •oco^ l 030oaoox>ooootoooo3 cr i ei ’~o ^ 

rH r-t rH rH CM t-h CM CM -r 30 <M O' -T lO W H H 

Diameter of the wheel. 

feet. 

• % •»c • 

*> yp^p DO DO CD CO 

00 OO DO do CD CD CD DO I> LO j> GO CiOOOrHrf 

Hi—'H *H *H 'HHHH rH —< r— r—i HH 

Power per sec. by sim¬ 
ple theorem. Art. 61. 

03 

£2 

o 

C Cl O CD CD 

t'* CD • • • • • Ci rH • • • • • QQ • • 

Cub. feet expended per 
sec. abating for fric¬ 
tion by conjecture. 

! cub. ft. 

oo co r>* 

GO ‘O rH rH DO CD 

CO CO DO © CO 

Velocity of water per 
second, by theory. 

feel. 

12.9 

11.17 

12.16 

14.4 

• 

13.8 

15.79 

14.96 

26.73 

. . 

* * 

• • 

16.2 

16 2 

24.3 
25.63 

14 

11.4 

Area of gate, abating 
for contraction occa¬ 
sioned by friction. 

feet. 

ir> >o ws r- 

00 (N ~r C* CO 

n rO CO rf 10 

• • • • . 

• • • • . 

lleau above the centre 
of the gate. 

feet. 

2.67 

1.9 

2.2 J 

3.1 

3 

3.83 

3.5 

• 

4 

4 

3 ’ 

2 

Virtual or effective de¬ 
scent of water. 

feet. 

20. 

19.2 

16.2 

16.6 

19.25 

17.8 

17.8 

11 

• • 

• • 

• • 

20.6 

21.5 

9.5 

10 

12.5 

• • 

No. of experiments. | 

rH d CO H DO CDt^OOCi O rH (M CO ^DOCDt^OO 

H rH »—' rH H r 1 rl Hh 


In the 3d, 4th, 13th, and 18th experiments, in the above table, there are 
two pair of stones to one water-wheel, the gears, &c. of which are shown 
by the braces. 















































































CHAP. III.] 


HYDRAULICS. 


12 i 


Observations continued from page 119. 

As we cannot attain to a mathematical exactness in 
those cases, and as it is evident that all tlie stones in the 
foregoing experiments have been working with too little 
power, because it is known that a pair of good burr stones 
of 5 feet diameter will grind, sufficiently well, about 125 
bushels in 24 hours—that is, 5.2 bushels in an hour, 
which would require 6.4 of power per second—we may, 
for the sake of simplicity, say 6 cubochs, when 5 feet 
stones grind 5 bushels per hour. Hence we deduce the 
following simple theorem for determining the size of the 
stones to suit the power of any given seat, or the power 
required to any size of a stone. 

THEOREM. 

Find the power by the theorem, in Art. 61; then di¬ 
vide the power by 6, which is the power required, by 1 
foot, and it will give you the area of the stone that the 
power will drive, to which add 1 foot for the eye, and 
divide by .7854, and the quotient will be the square of 
the diameter: or, if the power be great, divide by the 
product of the area of any sized stones you choose, mul¬ 
tiplied by six, and the quotient will be the number of 
stones the power will drive: or, if the size of the stone 
be given, multiply the area by 6 cubochs, and the pro¬ 
duct is the power required to drive it. 

EXAMPLE. 

1. Given 9 cubic feet per second, 12 feet perpendicu¬ 
lar, virtual, or effective descent, required the diameter 
of the stone suitable thereto. 

Then, by Art. 61, 9 x 12 = 108, the power, and 108-f- 
6 = 18, the area, and 18 x 1 -f- .7854 = 24.2, the root of 
which is 4.9 feet, the diameter of the stone required. 

2. The velocities of the mean circles of the stones in 
the table, are some below and some above 18 feet per se¬ 
cond, the mean of them all being nearly 18 feet; there¬ 
fore, I conclude that 18 feet per second is a good veloci¬ 
ty, in general, for the mean circle of any sized stone. 


122 


HYDRAULICS. 


[CHAP. III. 


Of the different quantity of Surfaces that are passed by 

Mill-stones of different diameters with different veloci¬ 
ties . 

Supposing the quantity ground by mill-stones, and the 
power required to turn them, to be as the passing sur¬ 
faces of their faces, each superficial foot that passes over 
another foot requires a certain power to grind a certain 
quantity: to explain this, let us premise, 

1. The circumferences and diameters of circles are di¬ 
rectly proportional. That is, a double diameter gives 
a double circumference. 

2. The areas of circles are as the squares of their di¬ 
ameters. That is, a double diameter gives 4 times the 
area. 

3. The square of the diameter of a circle, multiplied 
by .7854, gives its area. 

4. The square of the area of a mill-stone, multiplied 
by its number of revolutions, gives the surface passed. 
Consequently, 

5. In stones of unequal diameters, revolving in equal 
times, their passing surfaces, quantity ground, and power 
required to drive them, will be as the squares of their 
areas, or as the biquadrate of their diameters. That is, 
a double diameter will pass 16 times the surface.* 

6. If the velocity of their mean circles or circumfe¬ 
rences be equal, their passing surfaces, quantity ground, 
and power required to move them, will be as the cubes 
of their diameters.f 

7. If the diameters and velocities be unequal, their 
passing surfaces, and quantity ground, &c., will be as 

* The diameter of a 4 feet stone squared, multiplied by .7854, equal 12.56, its 
area: which squared, is 157.75 feet, the surface passed at one revolution: and 8 
multiplied by 8 equal 64, which multiplied by .7854, equal 50.24, being the area 
of an 8 feet stone, which squared is 2524.04, the surface passed, which surfaces 
are as 1 to 16. 

f Because the 8 feet stone will revolve only half as often as the 4 feet; there¬ 
fore, their quantity of surface passed, &c., can only be half as much more as it 
was in the last case; that is, as 8 to 1. 


CHAP. III.] 


HYDRAULICS. 


123 


tlie squares of their areas multiplied by their revolu¬ 
tions. 

8. If their diameters be equal, the quantity of sur¬ 
faces passed, &c., is as their velocities or revolutions 
simply. 

But we have been supposing theory and practice to 
agree strictly, which they will by no means do in this 
case. To the quantity ground, and the proportion of 
power used by large stones more than by small ones, 
the ratio assigned by the theory will not apply; because 
the meal having to pass a greater distance through the 
stone, is operated upon oftener, which operation must 
be lighter, else it will he overdone; large stones may, 
therefore, be made to grind equal quantities with small 
ones, and with equal power, and to do it with less 
pressure; therefore, the Hour will be better.* See Art. 
111 . 

From these considerations, added to experiments, I 
conclude, that the power required and quantity ground, 
will he nearly as the area of the stones multiplied into 
the velocity of the mean circles, or, which is nearly the 
same, as the squares of their diameters. But if the ve¬ 
locities of their mean circles or circumferences be equal, 
then it will be as their areas simply. 

On these principles I have calculated the following 
table, showing the power required, and quantity ground, 
both by theory, and what I suppose to be the most 
correct practice. 

* A French author (M. Fabre) says that he has found by experiments that to 
produce the best flour, a stone 5 feet diameter should revolve between 48 and G1 
times in a minute. This is much slower than the practice in America, but we 
may conclude that it is best to err on the side of a slower than of a faster motion 
than that of common practice; especially when the power is too small for the 
size of the stone. 




124 


HYDRAULICS 


[CHAP. Ill 


A TABLE 

OF THE AREA OF MILLSTONES 

or 

DIFFERENT DIAMETERS, 

And of the power required to move them with a mean velocity of 18 feet per 

second, &c. 


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feet. 

s. t. 

cuhs. 

feet. 


sup. ft. 

lbs. 

cuhs. 

lbs. 

lbs. 

3.5 

8.62 

51.72 

7.777 

138.8 

10312 

1.49 

33.1 

2.3 

2.45 

3.75 

9.99 

59.94 







2.8 

4. 

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69.36 

8.888 

121.5 

16236 

2.3 

52. 

3.1 

3.2 

4.25 

13.18 

78. 







3.6 

4.5 

14.9 

89.4 

9.99 

108.1 

23999 

3.46 

77. 

4. 

4.05 

4.75 

16.71 

100.26 







4.5 

5. 

18.63 

111.78 

11.09 

97.4 

34804 

5. 

111.78 

5. 

5. 

5.25 

20.64 

123.84 







5.53 

5.5 

22.76 

136.5 







6.05 

5.75 

24.96 

153.7 





y 


6.6 

6. 

27.27 

163.6 

13.37 

80.7 

60012 

8.6 

192. 

7.3 

7.2 

6.25 

29.67 

178. 







7.8 

6.5 

32.18 

196. 







8.4 

6.75 

34.77 

208.6 







9.1 

7. 

37.48 

225. 

15.55 

69.4 

97499 

14.06 

313. 

10. 

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1 

2 

3 

4 

5 

6 

7 

8 

9 

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Note. One foot is deducted for the eye in each stone, and the reason why, in 
the 7th column, the quantity ground is not exactly as the cubes of the diameter of 
the stones, and, in the 9th column, not exactly as the squares of its diameter, is 
the deduction for the eye, which being equal in each stone, destroys the proportion. 

The engine of a paper-mill, roll 2 feet diameter, 2 feet long, revolving 160 times 
in a minute, requires equal power with a 4 feet stone, grinding 5 bushels an hour. 

































CHAP. III.] HYDRAULICS. 125 

I have now laid down in Arts. 61, 62 and 63, a theory 
for measuring the power of any mill-seat, and for as¬ 
certaining the quantity of that power that mill-stones 
of different diameters will require, by which we can find 
the diameter of the stones to suit the power of the seat; 
and have fixed on six cuboclis of that power per second 
to every superficial foot of the mill-stone, as requisite to 
move the mean circle of the stone 18 feet per second, 
when in the act of grinding with moderate and sufficient 
feed; and have allowed the passing of 34804 feet per 
minute, to grind 5 lbs. in the same time, which is the ef- 
feet of the 5 feet stone in the table, by which, if right, 
we can calculate the quantity that a stone of any 
other size will grind with any given velocity. 

I have chosen a velocity of 18 feet per second for the 
mean circle of all stones, which is slower than the com¬ 
mon practice; but not too slow for making good flour. 
See Art. 111. Here will appear the advantage of large 
stones over small ones; for if we will make small stones 
grind as fast as large ones, we must give them such ve¬ 
locity as to heat the meal. 

But I must here inform the reader that the experi¬ 
ments from which I have deduced the quantity of pow¬ 
er to each superficial foot to be six cuboclis, have not 
been sufficiently exact to be relied on; but it will be 
easy for every intelligent mill-wright to make accurate 
experiments to satisfy himself as to this point,* 


* After having published the first edition of this work, I have been informed 
that, by accurate experiments made at the expense of the British government, 
it was ascertained that the power produced by 40,000 cubic feet of water descend¬ 
ing 1 foot, will grind and bolt 1 bushel of wheat. If this be true, then to find 
the quantity that any stream will grind per hour, multiply the cubic feet of water 
that it affords per hour, by the virtual descent, (that is, half of the head above 
the wheel, added to the fall after it ent rs an overshot-wheel,) and divide that 
product by 40,000, and the quotient will be the answer in bushels per hour that 
the stream will grind. 


EXAMPLE. 

Suppose a stream afford 32,000 cubic feet of water per hour, and the total fall 
19.28 feet; then, by the table for over-shot mills, Art. 73, the wheel should be 
16 feet diameter, head above the wheel 3.28 feet. Then half 3.28 = 1.64, which 
added to 16= 17.64 feet virtual descent, and 17.64 x 32000 = 563480, which 
divided by 40,000 gives 14.08 bushels per hour the stream will grind. 


126 


HYDRAULICS . 


[CHAP. III. 


ARTICLE 64. 

OF CANALS FOR CONVEYING WATER TO MILLS. 

In digging canals, we must consider that water will 
come to a level on its surface, whatever may be the 
form of the bottom. If we have once determined on 
the area of the section of the canal necessary to convey 
a sufficient quantity of water to the mill, we need only 
to keep to that area in the whole distance, without 
paying much regard to the depth or width, if there be , 
rocks in the way. Much expense may be oftentimes 
saved, by making the canal deep where it cannot easily 
be made wide enough, and wide where it cannot easily 
be made sufficiently deep. Thus, suppose we had de¬ 
termined it to be 4 feet deep, and 6 feet wide, then the 
area of its section will be 24. Let hg. 36, Plate IV., 
represent a canal, the line A B the level or surface of 
the water, C Dthe side, E F the bottom, A C the width 
6 feet, A E the depth, 4 feet. Then, if there be rocks 
at G, so that we cannot, without great expense, obtain 
more than 3 feet width, but can go 8 feet deep at a small 
expense; then 8x3= 24, the section required. Again, 
suppose a flat rock to be at H, so that we cannot, with¬ 
out great expense, obtain more than 2 feet depth, but 
can, with small expense, obtain 12 feet width; then 2 * 

12 = 24, the section required; and the water will come 
on equally well even if it were not more than .5 of a 
foot deep, provided it be proportionably wide. One dis¬ 
advantage, however, arises in having canals very shal¬ 
low in some places, because the water in dry seasons 
may be too low to rise over them; but if the water 
were always to be of one height, the disadvantage would 
be but trifling. The current will keep the deep places 
open, light sand or mud will not settle in them. This 
will seem paradoxical to some, but the experiment has 
been tried, and the fact established. 


CHAP. III.] 


HYDRAULICS. 


127 


ARTICLE 65. 

OF THE SIZE AND FALL OF CANALS. 

As to the size and fall necessary to convey any quan¬ 
tity of water required to a mill, I do not find any rule 
laid down for either. But in order to establish one, 
let us consider, that the size depends entirely upon the 
quantity of water, and the velocity with which it is to 
pass: therefore, if we can determine on the velocity, 
which I will suppose to be from 1 to 2 feet per second 
—but the slower the better, as there will be the less 
fall lost, we can find the size of the canal by the fol¬ 
lowing 


THEOREM. 

Divide the quantity required in cubic feet per se¬ 
cond by the velocity in feet per second, and the quo¬ 
tient will be the area of the section of the canal. Divide 
that area by the proposed depth, and the quotient is 
the width: or, divide by the width, and the quotient is 
the depth. 


PROBLEM I. 

Given, a 5 feet mill-stone, its mean circle to be moved 
with a velocity of 18 feet per second, on a seat of 10 
feet virtual, or effective, descent, required the size of 
the canal, with a velocity of 1 foot per second. 

Then, by theorem in Art. Go, the area of the stone 
18.63 feet multiplied by G cubochs of power, is equal 
111.78 cubochs for the power (in common practice, say 
112 cubochs,) which divided by 10, the fall, quotes 11. 
178 cubic feet required per second, which divided by 1, 
the velocity proposed per second, gives 11.178 feet, the 
area of the section, which divided by the depth pro¬ 
posed, 2 feet, gives 5.58 feet for the width. 


128 


HYDRAULICS. 


[CHAP. III. 


PROBLEM II. 

Given, a mill-stone 6 feet diameter to be moved with 
a velocity of 18 feet per second of its mean circle, to be 
turned by an undersliot-wheel on a seat of 8 feet per¬ 
pendicular descent, required the power necessary per 
second to drive them, and the quantity of water per se¬ 
cond to produce said power, likewise the size of the ca¬ 
nal to convey the water with a velocity of 1.5 feet per 
second. 

Then, by Art. 61, 8 feet perpendicular descent, on 
the undershot principle, is only = 4 feet virtual or effec¬ 
tive descent: and the area of the stone by the table (Art. 
63,) = 27.27 feet x 6 cubochs = 163.62 cubochs for the 
power per second, which divided by 4, the effective 
descent = 40.9 cubic feet, the quantity required per se¬ 
cond, which divided by the velocity proposed, 1.5 feet 
per seconds 27.26, for the area of the section of the 
canal, which divided by 2.25 feet, the depth of the ca¬ 
nal proposed = 12 feet, the width.* 

As to the fall necessary in the canal, I may observe, 
that the fall should be in the bottom of the canal, and 
none on the top, which should be all the way on a level 
with the water in the dam, in order that when the gate 
is shut down at the mill, the water may not overflow 
the banks, but stand at a level with the water in the 
dam; that is, as much fall as there is to be in the whole 
length of the canal, so much deeper must the canal be 
at the mill than at the dam. From many observations 
I conclude that about 3 inches to 100 yards will be suffi¬ 
cient, if the canal be long, but more will be requisite 
if it be short, and the head apt to run down when 
water is scarce; for the shallower the water, the great¬ 
er must be the velocity, and the more fall is required. 
—A French author, M. Fabre, allows one inch to 500 
feet. 

* An acre of a mill-pond contains 43560 cubic feet of water, for every foot of 
its depth. 

Suppose your pond contains 3 acres, and is 3 feet deep, then 43560 multiplied 
by 3, is equal 13UG80, which multiplied by 3, is equal 392010 cubic feet, its con¬ 
tents, which divided by the cubic feet your mill uses per second (say 10,) is 
equal 39204 seconds, or 10 hours, the time the pond will keep the mill going. 


CHAP. III.] 


HYDRAULICS. 


129 


ARTICLE 66. 

OF AIR-PIPES TO PREVENT TIGHT TRUNKS FROM BURSTING WHEN 

FILLED WITH WATER. 

When water is to be conveyed under ground or in a 
tight trunk below the surface of the water in the reser¬ 
voir, to any considerable distance, there must be air- 
pipes (as they have been called) to prevent the trunk 
from bursting. To understand their use, let us suppose 
a trunk 100 feet long, and 16 feet below the surface of the 
water; to fill which, a gate is to be drawn at one end, of 
equal size with the trunk. Then, if the water meet no 
resistance in passing to the other end, it acquires great 
velocity, which is suddenly to be stopped when the trunk 
is full. This great column of water, in motion, in this 
case, would strike with a force equal to that of a solid 
body of equal weight and velocity, the shock of which 
would be sufficient to break any trunk that ever was made 
of wood. Many having thought the use of these pipes to 
be to let out the air, have made them too small; so that 
they would vent the air fast enough to let the water in 
with considerable velocity, but would not admit the wa¬ 
ter fast enough to check its motion gradually; in which 
case they are worse than useless ; for if the air cannot 
escape freely, the water cannot enter freely, and the 
shock will be decreased by its resistance. 

Whenever the air has been compressed in the trunk 
by the water coming in, it has made a great blowing 
noise in escaping through the crevices, and, therefore, 
has been viewed as the cause of the bursting of the trunk: 
whereas it acted by its elastic principles, as a great pre¬ 
ventive against it. For, I apprehend, that if we were 
to pump all the air out of a trunk 100 feet long, and 3 
by 3 feet wide, and to let the water in with full force, 
it would burst, were it as strong as a cannon of cast me¬ 
tal; because, in that case, there would be 900 cubic feet 
of water, equal to 56250 lbs. pressed on by the weight of 
the atmosphere, with a velocity of 47 feet per second, to 
be suddenly stopped, the shock of which would be al¬ 
most irresistible. 

9 


130 


H Y D R A U L ICS. 


[chap. III. 

1 consider it best, therefore, to make an air-pipe of the 
full size of the trunk, every 20 or 30 feet; but this will 
depend much on the depth of the trunk below the sur¬ 
face of the reservoir, and upon other circumstances. 

Having now said what was necessary, in order the bet¬ 
ter to understand the theory of the power and principles 
of mechanical engines, and of water acting on water¬ 
wheels upon different principles, and, for establishing 
true theories of the motion of the different kinds of wa¬ 
ter-wheels, I here quote many of the celebrated Mr. 
Smeaton’s experiments, that the reader may compare 
them with the theories proposed, and judge for himself. 


ARTICLE 67. 

S MEATON’ S E XPERI MEN TS. 

•• An experimental Inquiry , read in the Philosophical /So¬ 
ciety in London , May 3 d, and 10 th, 1759, concerning the 
Natural Powers of Water to turn Mills and other ma¬ 
chines , depeyidinq on a circular Motion, by James Smea- 
ton , F. B. S. 

♦ 

“ What I have to communicate on this subject was 
•originally deduced from experiments made on working 
models, which I look upon as the best means of obtaining 
the outlines in mechanical inquiries. But in this case it 
is necessary to distinguish the circumstances in which a 
model differs from a machine in large; otherwise a mo¬ 
del is more apt to lead us from the truth than towards it. 
Hence the common observation, that a thing may do very 
well in a model that will not do in large. And, indeed, 
though the utmost circumspection be used in this way, 
the best structure of machines cannot be fully ascertained, 
but by making trials with them of their proper size. It 
is for this purpose that, though the models referred to, 
and the greatest part of the following experiments, were 
made in the years 1752 and 1753, yet I deferred offering 
them to the society till I had an opportunity of putting 



HYDRAULICS. 


131 


CHAP. HI.] 

the deductions made therefrom in real practice, in a va¬ 
riety of cases and for various purposes; so as to be able 
to assure the society that I have found them to answer.' 


PART I. 

CONCERNING UNDERSHOT WATER WHEELS. 

“ Plate XII. is a view of the machine for experiments 
on water wheels, wherein 

ABCD is the lower cistern or magazine for receiving 
the water after it has left the wheel, and for supplying 

DE, the upper cistern or head, wherein the water 
being raised to any height by a pump, that height is 
shown by 

FG, a small rod divided into inches and parts, with a 
float at the bottom to move the rod up and down, as 
the surface of the water rises and falls. 

HI is a rod by which the sluice is drawn, and stopped 
at any height required by means of 

K, a pin or peg, which fits several holes placed in the 
manner of a diagonal scale upon the face of the rod 
HI. 

GL is the upper part of the rod of the pump for draw¬ 
ing the water out of the lower cistern, in order to raise 
and keep up the surface thereof to its desired height in 
the head 1)E, thereby to supply the water expended by 
the aperture of the sluice. 

MM is the arch and handle of the pump, which is 
limited in its stroke by 

N, a piece for stopping the handle from raising the 
piston too high, that also being prevented from going 
too low, by meeting the bottom of the barrel. 

O is a cylinder upon which the cord winds, and which 
being conducted over the pulleys P and Q raises 

R ? the scale into which the weights are put for trying 
the power of the water. 

W the beam which supports the scale that is placed 
15 or 16 feet higher than the wheel. 


132 


HYDRAULICS. 


[CHAP. III. 

XX is the pump-barrel, 5 inches diameter and 11 
inches long. Y is the piston, and Z is the fixed valve. 

GV is a cylinder of wood, fixed upon the pump-rod, 
and reaches above the surface of the water; this piece 
of wood being of such thickness that its section is half 
the area of the pump-barrel, will cause the water to rise 
in the head as much while the piston is descending as 
while it is rising, and will thereby keep the gauge-rod 
FG more equally to its height. 

a a shows one of the two wires that serve as a direc¬ 
tor to the float, b is the aperture of the sluice, c a is 
a cant-board for canting the water down the opening 
c d into the lower cistern, c e is a sloping board for 
bringing back the water that is thrown up by the 
wheel. 

There is a contrivance for engaging and disengaging 
the Scale and weight instantaneously from the wheel, 
by means of a hollow cylinder on which the cord winds 
by slipping it on the shaft; and when it is disengaged, 
it is held to its place by a racket-wheel; for without 
this, experiments could not be made with any degree of 
exactness. 

The apparatus being now explained, I think it ne¬ 
cessary to assign the sense in which I use the term 
power. 

The word power is used in practical mechanics, I ap¬ 
prehend, to signify the exertion of strength, gravity, im¬ 
pulse, or pressure, so as to produce motion. 

The raising of a weight, relative to the height to 
which it can be raised in a given time, is the most pro¬ 
per measure of power. Or, in other words, if the weight 
raised be multiplied by the height to which it can be 
raised in a given time, the product is the measure of the 
power raising it; and, consequently, all those powers are 
equal. But note, all this is to be understood in case of 
•slow or equable motion of the body raised; for in quick, 
accelerated or retarded motions, the vis inertia of the 
matter moved will make a variation. 

In comparing the effects produced by water wheels 
with the powers producing them; or, in other words, to 


HYDRAULICS. 


133 


CHAP. III.] 

know what part of the original power is necessarily lost 
in the application, we must previously know how much 
of the power is spent in overcoming the friction of the 
machinery and the resistance of the air; also what is 
the real velocity of the water at the instant it strikes 
the wheel, and the real quantity of water expended in 
a given time. 

From the velocity of the water at the instant that it 
strikes the wheel, given; the height of the head pro¬ 
ductive of such velocity can be deduced from acknow¬ 
ledged and experienced principles of hydrostatics; so 
that by multiplying the quantity or weight of water 
really expended in a given time, by the height of head 
so obtained, which must he considered as the height from 
which that weight of water had descended, in that given 
time, we shall have a product equal to the original power 
of the water, and clear of all uncertainty that would 
arise from the friction of the water in passing small 
apertures, and from all doubts, arising from the differ¬ 
ent measure of spouting waters, assigned by different 
authors. 

On the other hand, the sum of the weight raised by the 
action of this water, and of the weight required to over¬ 
come the friction and resistance of the machine, multi¬ 
plied by the height to which the weight can be raised in 
the given time, the product will be the effect of that 
power; and the proportion of the two products will be 
the proportion of the power to the effect; so that by 
loading the wheel with different weights successively, 
we shall be able to determine at what particular load 
and velocity of the wheel the effect is a maximum. 


To determine the Velocity of the Water striking the Wheel. 

“ First, let the wheel be put in motion by the water, 
but without any weight in the scale; and let the number 
of turns in a minute be GO : now, it is evident, that were 
the wheel free from friction and resistance, that GO times 
the circumference of the wheel would be the space 
through which the water would have passed in a minute 


134 


HYDRAULICS. 


[CHAP. III. 

with that velocity wherewith it struck the wheel. But 
the wheel being encumbered with friction and resist¬ 
ance, and }^et moving GO .turns in a minute, it is plain, 
that the velocity of the water must have been greater 
than GO circumferences, before it met with the wheel. 
Let the cord now be wound round the cylinder, but con¬ 
trary to the usual way, and put as much weight in the 
scale as will, without any water, turn the wheel somewhat 
faster than GO turns in a minute, suppose 63, and call this 
the counter-weight; then let it be tried again with the 
water assisted by this counter-weight, the wheel, there¬ 
fore. will now make more than GO turns in a minute, sup¬ 
pose G4, hence we conclude the water still exerts some 
power to turn the wheel. Let the weight be increased 
so as to make G4I turns in a minute without the water, 
then try it with the water and the weight as before, and 
suppose it now make the same number of turns with the 
water, as without; namely, 64i, hence, it is evident, that 
in this case the wheel makes the same number of turns 

as it would with the water, if the wheel had no friction 

/ 

or resistance at all, because the weight is equivalent 
thereto; for if the counter-weight'were too little to over¬ 
come the friction, the water would accelerate the wheel, 

. and if too great it would retard it; for the water in this 
case becomes a regulator of the wheel’s motion, and the 
velocity of its circumference becomes a measure of the 
velocity of the water. 

In like manner, in seeking the greatest product or max¬ 
imum of effect; having found by trials what weight gives 
the greatest product, by simply multiplying the weight 
in the scale by the number of turns of the wheel, find 
what weight in the scale, when the cord is on the con¬ 
trary side of the cylinder, will cause the wheel to make 
the same number of turns, the same way, without water: 
it is evident that this weight will be nearly equal to all 
friction and resistance taken together; and, consequently, 
that the weight in the scale, with twice * the weight 

of the scale, added to the back or counter-weight, will 

»• 

* The weight of the scale makes part of the weight both ways, namely; both 
of the weight and counter-weight. 


HYDRAULICS. 


CHAP. III.] 



be equal to the weight that could have been raised, sup¬ 
posing the machine had been without friction or resist¬ 
ance, and which multiplied by the height to which it 
was raised, the product will be the greatest effect of that 
power. 


The quantity of Water expended is found thus :— 

“The pump was so carefully made, that no water 
escaped back through the leathers, it delivered the same 
quantity each stroke, whether quick or slow, and by as¬ 
certaining the quantity of 12 strokes and counting the 
number of strokes in a minute that was sufficient to keep 
the surface of the water to the same height, the quan¬ 
tity expended was found. 

These things will be farther illustrated by going over 
the calculations of one set of experiments. 


Specimen of a Set of Experiments. 


The sluice drawn to the first hole. 

The water above the floor of the sluice, 30 inches. 
Strokes of the pump in a minute, 391 

The head raised by 12 strokes, 21 

The wheel raised the empty scale and made ) gQ 
turns in a minute, 

With a counter-weight of one lb. 8 oz. it 
made, 

Ditto, tried with water. 



No. 

lbs. oz. 

turns in a min. 

product. 

1 

4:0 

45 

180 

2 

5:0 

42 

210 

3 

6:0 

36} 

217} 

4 

7:0 

33f 

236} 

5 

8:0 

30 

240 max. 

6 

9:0 

26} 

238} 

l 

10:0 

22 

220 

8 

11:0 

16} 

181} 

9 

12:0 

*ceased workin 

or 

t'* 


* When the wheel moves so slowly as not to rid the water as fast as supplied 
by the sluice, the accumulated water falls back upon the aperture, and the 
wheel immediately ceases moving. This note of the author argues in favour of 
drawing the gate near the float. 


136 HYDRAULICS. [CHAP. III. 

Co an ter-weight for 30 turns without water 2 oz. in 
the scale. 

N. B. the area of the head was 105.8 square inches, 
weight of the empty scale and pulley 10 ounces, circum¬ 
ference of the cylinder 9 inches, and circumference of 
the water-wheel 75 inches. 

Reduction of the above Set of Experiments. 

The circumference of the wheel 75 inches multiplied 
by 86 turns, gives 6450 inches for the velocity of the 
water in a minute, l-60tli of which will be the velocity 
in a second, equal to 107.5 inches, or 8-96 feet, which 
is due to a head of 15 inches,* and this we call the 
virtual or effective head. 

The area of the head being 105.8 inches, this multi¬ 
plied by the weight of water of one cubic inch, equal 
to the decimal of .579 of the ounce avoirdupois, gives 
61.26 ounces for the weight of as much water as is con¬ 
tained in the head upon one inch in depth, 1-10th of 
which is 3.83 lbs.; this multiplied by the depth, 21 
inches, gives 80.43 lbs. for the value of 12 strokes, and 
by proportion 391 (the number made in a minute) will 
give 264.7 lbs., the weight of water expended in a 
minute. 

Now, as 264.7 lbs., of water may be considered as 
having descended through a space of 15 inches in a 
minute, the product of these two numbers 3970, will 
express the power of the water to produce mechanical 
effects; which are as follows:— 

The velocity of the wheel at a maximum, as appears 
above, was 30 turns in a minute; which, multiplied by 
9 inches, the circumference of the cylinder, makes 270 
inches: but as the scale was hung by a pulley and dou¬ 
ble line, the weight was only raised half of this, namely; 
135 inches. 

This is determined by the common maxim of hydrostatics; that the velo¬ 
city of spouting water is equal to the velocity that a heavy body would acquire 
in falling from the height of the reservoir; and is proved by the rising of jets 
to the height of their reservoirs nearly. 


CHAP. III.] 


HYDRAULICS. 


137 


Tlie weight in the scale at the 
maximum, 

Weight of the scale and pul¬ 
ley, 

Counter-weight, scale and pul¬ 
ley, 

Sum of the resistance, lbs. 9 6, or 9.375 lbs. 

Now, as 9.375 lbs. are raised 135 inches, these two 
numbers being multiplied together produce 1266, which 
expresses the effect produced at a maximum: so that 
the proportion of the power to the effect is as 3970: 
1266, or as 10 : 3.18. 

But though this be the greatest single effect produci¬ 
ble from the power mentioned, by the impulse of the 
water upon an undershot-wheel; yet, as the whole power 
of the water is not exhausted thereby, this will not 
be the true ratio between the power and the sum of all 
the effects producible therefrom; for, as the water must 
necessarily leave the wheel with a velocity equal to the 
circumference, it is plain that some part of the power 
of the water must remain after leaving the wheel. 

The velocity of the wheel at a maximum is 30 turns 
a minute; and, consequently, its circumference moves at 
the rate of 3.123 feet per second, which answers to a 
head of 1.82 inches; this being multiplied by the ex¬ 
pense of water in a minute; namely, 264.7 lbs., produces 
481 for the power remaining: this being deducted from 
the original power, 3970, leaves 3489, which is that part 
of the power that is spent in producing the effect 1266; 
so that the power spent, 3489, is to its greatest effect 
1266, as 10 : 3.62, or as 11 : 4. 

The velocity of the water striking the wheel 86 turns 
in a minute, is to the velocity at a maximum 30 turns a 
minute, as 10 : 3.5, or as 20 to 7, so that the velocity of 
the whefel is a little more than l-3d of the velocity of 
the water. 

The load at a maximum has been shown to be equal 
to 9 lbs. 6 oz., and that the wheel ceased moving with 12 


lbs. oz. 
8 0 

0 10 

0 12 



HYDRAULICS. 


138 


[ciiap. III. 


lbs. in the scale; to which, if the weight of the scale be 
added, namely, 10 oz.,* the proportion will be nearly as 3 
to 4, between the load at a maximum and that by which 
the wheel is stopped.f 

It is somewhat remarkable that though the velocity 
of the wheel in relation to the water turns out greater 
than l-3d of the velocity of the water, yet the impulse 
of the water in case of the maximum is more than dou¬ 
ble of what is assigned by theory; that is, instead ol 
4-9ths of the column, it is nearly equal to the whole 
col umn. J 

It must be remembered, therefore, that in the present 
case, the wheel was not placed in an open river, where 
the natural current, after it has communicated its im¬ 
pulse to the float, has room on all sides to escape, as the 
theory supposes; but in a conduit or race, to which the 
float being adapted, the water cannot otherwise escape 
than by moving along with the wheel. It is observable 
that a wheel working in this manner, as soon as the wa¬ 
ter meets the float, it, receiving a sudden check, rises 
up against the float, like a wave against a fixed object, 
insomuch, that when the sheet of water is not a quarter 
of an inch thick before it meets the float, yet this sheet 
will act upon the whole surface of a float, whose height 
is three inches; consequently, were the float no higher 
than the thickness of the sheet of water, as the theory 
also supposes, a great part of the force would be lost 
bv the water dashing over it. 

v o 


* The resistance of the air in this case ceases, and the friction is not added, 
as 12 lbs. in the scale was sufficient to stop the wheel after it had been in full 
motion, and, therefore, somewhat more than a counterbalance for the impulse 
of the water. 

f I may here observe that it is probable that if the gate of the sluice had been 
drawn as near the float-boards as possible, (as is the practice in America, where 
water is applied to act by impulse alone,) that the wheel would have continued 
to move until loaded with times the weight of the maximum load, namely, 9 
lbs. 6 oz. multiplied by 1£, equal to 14 lbs. 1 oz. It would then have agreed 
with the theory established, Art. 41. This, perhaps, escaped the notice of our 
author. 

t This observation of the author I think a strong confirmation of the truths of 
the theory established, Art. 41, where the maximum velocity is made to be .577 
parts of the velocity of the water, and the load to be 2-3ds the greatest load : 
for if the gate had been drawn near the floats, the greatest load would pro¬ 
bably have been 14 lbs. 1 oz., or as 3 to 2 of the maximum load. 


II YDRAULICS. 


CHAP, III.] 


139 


Iri confirmation of what is already delivered, 1 have 
subjoined the following table, containing the result of 
27 experiments made and reduced in the manner above 
specified. What remains of the theory of undershot 
wheels will naturally follow from a comparison of the 
different experiments together. 





140 


HYDRAULICS 


[CHAP. HI 


A TABLE OF EXPERIMENTS. 

No. 1. 


Number. 

Height of the water in the cistern. 

Turns of the wheel, unloaded. 

Virtual head deduced therefrom. 

Turns at a maximum. 

Load at the equilibrium. 

Load at the maximum. 

Water expended in a minute. 

Power. 

Effect. 

Ratio of the power and effect. 

Ratio of the velocities of the water and 

wheel. 

Ratio of the load at the equilibrium to 

the load at the maximum. 

Experiments. 


in 


inch. 


lb. oz. 

lb. oz. 

lbs. 







1 

33 

88 

15.85 

30 

13 

10 

10 9 

275 

4358 

1411 

10:3.24 

10:3.4 

10:7.75 


2 

30 

86 

15. 

30 

12 

10 

9 6 

264.7 

3970 

1266 

10:3.2 

10:3.5 

10:7.4 

> 

3 

27 

82 

13.7 

28 

11 

2 

8 6 

243 

3329 

1044 

10:3.15 

10:3.4 

10:7.5 

c-t- 

4 

24 

78 

12.3 

27.7 

9 

10 

7 5 

235 

2890 

901.4 

10:3.12 

10:3.55 

10:7.53 

sr 

5 

21 

75 

11.4 

25.9 

8 

10 

6 5 

214 

2439 

735.7 

10:3.02 

10:3.45 

10:7.32 

h - 1 

6 

18 

70 

9.95 

23.5 

6 

10 

5 5 

199 

1970 

561.8 

10:2.85 

10:3.36 

10:8.02 

Ui 

c-t- 

7 

15 

65 

8.54 

23.4 

5 

2 

4 4 

178.5 

1524 

442.5 

10:2.9 

10.3.6 

10:8.3 

ST 

o 

8 

12 

60 

7.29 

22 

3 

10 

3 5 

161 

1173 

328 

10:2.8 

10:3.77 

10:9.1 

<tT 

9 

9 

52 

5.47 

19 

2 

12 

2 8 

134 

733 

213.7 

10:2.9 

10:3.65 

10:9.1 


10 

6 

42 

3.55 

16 

1 

12 

1 10 

114 

404.7 

117 

10:2.82 

10:3.8 

10:9.3 


11 

24 

84 

14.2 

30.75 

13 

10 

10 14 

342 

4890 

1505 

10:3.07 

10:3.66 

10:7.9 


12 

21 

81 

13.5 

29 

11 

10 

9 6 

297 

4009 

1223 

10:3.01 

10:3.62 

10:8.05 

> 

13 

18 

72 

10.5 

26 

9 

10 

8 7 

285 

2993 

975 

10:3.35 

10:3.6 

10:8.75 

C“f 

14 

15 

691 9.6 

25 

7 

10 

6 141 277 

2659 

774 

10:2.92 

10:3.62 

10:9. 

:r 

15 

12 

63 

8.0 

25 

5 

10 

4 14 

234 

1872 

549 

10:2.94 

10:3.97 

10:8.7 

i 

to 

16 

9 

56 

6.37 

23 

4 

0 

3 13 

201 

1280 

390 

10:3.05 

10:4.1 

10:9.5 

• 

17 

6 

40 

i 4.25 

21 

2 8 

2 4 

167.5 

712 

212 

10:2.98 

10:4.55 

10:9. 


16 

15 

72 

10.5 

29 

11 

10 

9 6 

357 

3748 

1201 

10:3.23 

10:4.02 

10:8.05 


19 

12 

66 

8.75 

26.75 

8 

10 

7 6 

330 

2887 

878 

10:3.05 

10:4.05 

10:8.1 

GC 

20 

9 

56 

6.8 

24.5 

5 

8 

5 0 

255 

1734 

541 

10:3.01 

10:4.22 

10:9.1 

£- 

• 

*21 

6 

46 

4.7 

23.5 

3 

2 

3 0 

228 

1064 

317 

10:2.99 

10:4.9 

10:9.6 


2*2 

12 

66 

9.3 

27 

9 

2 

8 6 

359 

3338 

1006 

10:3.02 

10:3.97 

10:9.17 

* 

23 S 

56 

6.8 

26.25 

6 

2 

5 13 

332 

2257 

686 

10:3.04 

10:4.52 

10:9.5 

rj* 

24 C 
1 

46 

4.7 

24.5 

3 

12 

3 6 

262 

1231 

385 

10:3.13 

10:5.1 

10:9.35 


25 £ 

6f 

) 7.29 

27.3 

6 

12 

6 6 

355 

2588 

783 

10:3.03 

10:4.55 

10:9.45 

Ox 

26 ( 

>5( 

5.03 

24.6 

4 

6 

4 1 

307 

1544 

456 

10:2.92 

10:4.9 

10:9.3 

sr 

i 27 i ' 

j 5( 

J 5.03 

26 

4 

15 

4 £ 

360 

1811 

534 

10:2.95 

10:5.2 

10:9.25 

p 

1 

2 

3 

4 

5 

1 6 

7 

8 

9 

10 

11 

1 12 

13 











































































































































































CHAP. III.] 


HYDRAULICS. 


141 


Maxims and observations deduced from the foregoing 

table of experiments. 

Max. I. That the virtual or effective head being the 
same, the effect will be nearly as the quantity of water 
expended. 

This will appear by comparing the contents of the 
columns 4, 8, and 10, in the foregoing sets of experi¬ 
ments, as for 

Example I. taken from JVo. 8 and 25; namely :— 

No. Virtual head. Water expended. Effect. 

8 7.29 161 328 

25 7.29 355 785 

Now, the heads being equal, if the effects be propor¬ 
tioned to the water expended, we shall have by maxim 
1, as 1G1 : 355 : : 328 : 723; but 723 falls short of 785, 
as it turns out in experiment, according to No. 25 by 
62. The effect, therefore, of No. 25, compared with No. 
8, is greater than, according to the present maxim, in 
the ratio of 14 to 13. # 

The foregoing example, with four similar ones, may 
be seen at one view in the following table. 

* If the true maximum velocity of the wheel be .577 of the velocity of the 
water, and the true maximum load be 2-3ds of the whole column, as shown in 
Art. 42; then the effect will be to the power in the ratio of 10U to 38, or as 10 
to 3.8, a little more than appears by the table of experiments in columns 9 and 
10 : the difference is owing to the disadvantageous application of the water on the 
wheel in the model. 


142 


HYDRAULICS 


[chap. Ill 


TABLE OF EXPERIMENTS. 
NO. II. 


— -— — - - - - - 1 “ ' 


<M 



i'- 


CO 

a 

05 

r- 

N 

^ Proportional 

T“^ 


CO 

• • 

r-H 

' 1 

variation. 

T 

«-4 

00 

00 

00 



<M 

CO 

1—t 

i> 





T** 

Variation. 

** 

co 

+ 

J[ 

1 

00 

+ 

+ 

CO 


H 

r~i 

CM 




T—1 





CO 

tM 





o« 

tM 

o 

to 

CO’ 



i-H 

e- 

CO 

kO 

* 

X 

oo 

o 


e- 

o 


Cm 


-* 

< 

50 

vl 

CO 

.. 

• • 

CO 



. # 

• • 


• • 

• • 

< 

o 

e- 

CM 

<M 

o 


o 

o 

CO 

to 

to 

•-H 

CO 

CO 

CO 

Cl 

CO 

1 ^5 

Q 


. » 

• • 

.. 

• • 


50 

50 

00 

1— 

CJ 

to 

00 

>o 

CM 

O 



tM 

CM 

tM 

M . 

E fleet. 

00 o 

o o 

t tO 

1- 50 

o •«* 


CM 00 

N »—« 

-t 1 00 

*-H 00 

50 CO 


CO t" 

05 (M 

50 co 

CO CO 

rf 50 



rH 




Expense of water. 

r-1 LO 

CD lO 

50 h- 

oo *o 

50 <M 

50 CO 

00 tM 
tM CD 

e~ o 
o to 

H CO 

CM CO 

C4 CO 

CM <M 

CO CO 

Virtual head. 

05 05 

<n <m 

io »n 

o_o 

00 oq 


CO CO 

o o 

t-’ t- 

r—t r—< 

CO to 

'tf ^ 

50 »d 

V 

00 »o 

CO 00 

tM CO 

«-i ~r 

to t'- 

No. Table 1. 


r-i r-S 

t CM CM 

<M <M 

<M tM 




— 


- 

Examples. 

•*—* 

CO 

i-H 

2d. 

• 

-a 

CO 

4th. 

5th. 





















































HYDRAULICS. 


143 


CHAP. III.] 

By this table of experiments, it appears that some fall 
short of, and others exceed, the maximum, and all agree 
as nearly as can be expected in an affair where so many 
different circumstances are concerned; therefore, we may 
conclude the maxim to be true. 

Max. II. That the expense of the water being the 
same, the effect will be nearly as the height of the vir¬ 
tual or effective head. 

This also will appear by comparing the contents of 
columns 4, 8, and 10, in any of the sets of experiments. 

Example I. of No. 2 and No. 24. 

No. Virtual Head. Expense. Effect. 

2 15 264.7 1266 

24 4.7 262 385 

Now, as the expenses are not quite equal, we must 
proportion one of the effects accordingly, thus:— 

By maxim I. 262 : 264.7 :: 385 : 389 

And by max. II. 15 : 4.7 :: 1266 : 397 

s * _ 

Difference, 8 

The effect, therefore, of No. 24, compared with No. 
2, is less than according to the present maxim, in the 
ratio of 49 : 50. 

Max. III. That the quantity of water expended being 
tlie same, the effect is nearly as the square root of its 
velocity. 

This will appear by comparing the contents of co¬ 
lumns 3, 8, and 10, in any set of experiments; as for 


Example I. of No. 2. with No. 24; namely :— 


No. 

Turns in a minute. 

Expense. 

Effect. 

9 

86 

264.7 

1266 

24 

48 

262 

385 


The velocity being as the number of turns, we shall 
have, 



144 


HYDRAULICS. [CHAP. III. 

: 389 
: 394 


Difference, 5 

The effect of No. 24, compared with No. 2, is less 
than by the present maxim in the ratio of 78 : 79. 

Max. IV. The aperture being the same, the effect will 
be nearly as the cube of the velocity of the water. 

This also will appear by comparing the contents of 
columns 3, 8, and 10, as for 


By maxim I. 

And by max. III. 


2G2 : 264.7 
86 2 48 5 

7396 : 2304 


:: 385 

::12C6 


Example , No. 1 and No. 10; namely :— 

No. Turns. Expense. Effect. 

1 88 275 1411 

10 42 114 117 

Lemma. It must here be observed that if water pass 
out of an aperture in the same section, but with diffe¬ 
rent velocities, the expense will be proportional to the 
velocity; and, therefore, conversely, if the expense be 
not proportional to the velocity, the section of water is 
not the same. 

Now, comparing the water discharged with the turns 
of Nos. 1 and 10, we shall have 88 : 42 :: 275 : 131.2; 
but the water discharged by No. 10 is only 114 lbs., 
therefore, though the sluice was drawn to the same 
height in No. 10 as in No. 1, yet the section of the 
water passing out was less in No. 10 than in No. 1, in 
the proportion of 114 to 131.2; consequently, had the 
effective aperture or section of the water been the same 
in No. 10 as in No. 1, so that 131.2 lbs. of water had 
been discharged instead of 114 lbs. the effect would have 
been increased in the same proportion; that is, 


By lemma, 

88 

42 :: 

275 : 131.2 

By maxim I., 

114 

131.2 :: 

117 : 134.5 

And by max. IV., | 

88* 

681472 

42 n 

74088 j :: 

1411 : 153.5 


Difference, 19 





HYDRAULICS. 


145 


CHAP. III.] 

The effect, therefore, of No. 10, compared with No. 1, 
is less than it ought to be, by the present maxim, in 
the ratio of 7 : 8. 


OBSERVATIONS. 

“Observ. 1st. On comparing columns 2 and 4, table 
I., it is evident that the virtual head bears no certain 
proportion to the head of water, but that when the aper¬ 
ture is greater, or the velocity of the water issuing there¬ 
from less, they approach nearer to a coincidence; and 
consequently, in the large opening of mills and sluices, 
where great quantities of water are discharged from mo¬ 
derate heads, the head of water and virtual head deter¬ 
mined from the velocity will nearer agree, as experience 
confirms. 

Observ. 2d. Upon comparing the several proportions 
between the powers and effects in column 11th, the most 
general is that of 10 to 3; the extremes are 10 to 3.2 
and 10 to 2.8; but as it is observable, that where the 
quantity of water or the velocity thereof is great, that 
is, where the power is greatest, the 2d term of the ratio 
is greatest, also; we may, therefore, w r ell allow the pro¬ 
portion subsisting in large works as 3 to 1. 

Observ. 3d. The proportion of velocities between the 
water and wheel in column 12 is contained in the limits 
of 3 to 1 and 2 to 1; but as the greater velocities ap¬ 
proach the limits of 3 to 1, and the greater quantity 
of water approaches to that of 2 to 1, the best general 
proportion will be that of 5 to 2.* 

Observ. 4th. On comparing the numbers in column 
13, it appears that there is no certain ratio between the 


* I will here observe, that Mr. Smeaton may be mistaken in his conclusion, 
that the best general ratio of the velocity of the water to that of the wheel will 
be as 5 to 2, because, we may observe, that, in the first experiment, where the 
virtual head was 15.85 inches, and the gate drawn to the first hole, the ratio is 
as 1U : 3.4. But in the last experiment, where the head was 5.03 inches, and 
the gate drawn to the sixth hole, the ratio is as 10 : 5.2: and that the 2d term 
of the ratio increases, gradually, as the head decreases, and quantity of water 
increases; therefore, we may conclude, that, in the large openings of mills, the 
ratio may approach 3 to 2, which will agree with the practice and experiments 
of many able mill-wrights of America, and many experiments I have made on 
mills. And as it is better to give the wheel too great than too little velocity. 
I conclude, the wheel of an undershot mill must have nearly two-thirds of the 
velocity of the water to produce a maximum effect. 

10 


HYDRAULICS. 


14(3 


[chap. III. 


load that the wheel will carry at its maximum, and what 
will totally stop it; but that they are contained within 
the limits of 20 to 19 and of 20 to 15; but as the effect ap¬ 
proaches nearest to the ratio of 20 to 15 or of 4 to o, when 
the power is greatest, whether by increase of velocity or 
quantity of water, this seems to be the most applicable 
to large works; but as the load that a wheel ought to 
have in order to work to the best advantage, can be as¬ 
signed by knowing the effect it ought to produce, and 
the velocity it ought to have in producing it, the exact 
knowledge of the greatest load that it will bear is of less 
consequence in practice.* 

It is to be noted, that in almost all of the examples 
under the last three maxims, (of the four preceding,) the 
effect of the less power falls short of its due proportion 
to the greater, when compared by its maxim. And 
hence, if the experiments be taken strictly, we must 
infer that the effects increase and diminish in a higher 
ratio than those maxims suppose; but as the deviations 
are not very considerable, the greatest being about l-8th 
of the quantity in question, and as it is not easy to make 
experiments of so compound a nature with absolute pre¬ 
cision, we may rather suppose that the less power is at¬ 
tended with some friction, or works under some disad¬ 
vantage, not accounted for; and, therefore, we may con¬ 
clude, that these maxims will hold very nearly, when 
applied to works in large. 

After the experiments above mentioned were tried, 
the wheel which had 24 floats was reduced to 12, which 
caused a diminution in the effect on account of a greater 
quantity of water escaping between the floats and the 
lioor; but a circular sweep being adapted thereto, of 
such a length that one float entered the curve before the 
preceding one quitted it, the effect came so near to the 
former, as not to give hopes of increasing the effect by 
increasing the number of floats past 24 in this particular 
wheel. 

* Perhaps the author is here again deceived by the imperfection of the model, 
for had the water been drawn close to the float, the load that would totally stop 
the wheel would always be equal to the column of water acting on the wheel. 
See the note, page 70. The friction of the shute and air destroyed great part 
of the force of his small quantity of water. 


CHAP. III.] 


hydraulics. 


147 


PART II. 


ARTICLE 68. 

* 

CONCERNING OVERSHOT WHEELS. 

“ Iii the former part of this essay we have considered 
the impulse of a confined stream acting on undershot 
wheels; we now proceed to examine the power and ap¬ 
plication of water when acting by its gravity on over¬ 
shot wheels. 

It will appear in the course of the following deduc¬ 
tions that the effect of the gravity of descending bodies 
is very different from the effect of the stroke of such as 
are non-elastic, though generated by an equal mechani¬ 
cal power. 

The alterations of the machinery already described 
to accommodate the same for experiments on overshot 
wheels, were principally as follows:— 

Plate XII. The sluice I b being shut down, the rod 
II I was taken off. The undershot water-wheel was 
taken off the axis, and instead thereof, an overshot 
wheel of the same size and diameter was put in its 
place. Note, this wheel was 2 inches deep in the shroud 
or depth of the bucket; the number of buckets was 36. 

A trunk for bringing the water upon the wheel was 
fixed, acording to the dotted lines, f g; the aperture 
was adjusted by a shuttle, which also closed up the 
outer end of the trunk, when the water was to be 
stopped. , 


148 


HYDRAULICS. 


[cnAP. III. 


Specimen of a set of experiments. 

Head 6 inches—14| strokes of the pump in a minute, 12 
ditto = 80 lbs.*—weight of the scale (being wet) 10L 
ounces. 

Counter weight for 20 turns, besides the scale, 3 ounces. 


No. 

wt. in the scale. 

turns. 

product. Observations. 

1 

0 

60 

-1 

1 threw most part 

2 

1 

56 


> of the water out 

3 

2 

52 

-J 

\ of the wheel. 

4 

3 

49 

14T 1 

| received the wa- 

5 

4 

4T 

188 i 

f ter more quietly. 

6 

5 

45 

225 

ry 

7 

6 

42J 

255 


8 

7 

l 

41 

28T 


9 

8 

384 

308 


10 

9 

364 

3284 


11 

10 

354 

355“ 


12 

11 

32* 

3604 


13 

12 

314 

3T5“ 


14 

13 

28J 

3T04 


15 

14 

2T4 

385“ 


16 

15 

26" 

390 


IT 

16 

24i 

392 


18 

IT 

22* 

386* 


19 

20 

18 

21* 

3914 


19 

20* 

3944 

> . 

21 

20 

19| 

395 

> maximum. 

22 

21 

184 

3834 

J 

23 

24 

99 

tmm 4mJ 

23 

18 

overset 

396 worked irregularly, 
by its load. 


* The small difference in the value of 12 strokes of the pump from the former 
experiments, was owing to a small difference in the length of the stroke, occa¬ 
sioned by the warping of the wood. 


CHAP. III.] 


HYDRAULICS. 


149 


Reduction of the preceding specimen . 

“In these experiments the head being 6 inches, and 
the height of the wheel 24 inches, the whole descent 
will be 30 inches; the expense of water was 14] strokes 
of the pump in a minute, whereof 12 contained 80 lbs.; 
therefore, the water expended in a minute was 9Of lbs., 
which, multiplied by 30 inches, give the power s 2900. 

If we take the 20th experiment for the maximum, we 
shall have 20] turns in a minute, each of which raised 
the weight 4] inches; that is, 93.37 inches in a minute. 
The weight in the scale was 19 lbs., the weight of the 
scale 10-1 oz *> the counter-weight 3 oz. in the scale, which, 
with the weight of the scale, 10]- oz., make in the whole 
20] lbs., which is the whole resistance or load; this, 
multiplied by 93.37, makes 1914 for the effect. 

The ratio, therefore, of the power and effect will be 
as 2900 : 1914, or as 10 : 6.G, or as 3 to 2, nearly. 

But if we compute the power from the height of the 
wheel only, we have 96] lbs. x 24 inches = 2320 for the 
power, and this will be to the effect as 2320 :1914, or as 
10 : 8.2, or as 5 to 4, nearly. 

The reduction of this specimen is set down in No. 9 
of the following table, and the rest were deduced from a 
similar set of experiments, reduced in the same manner. 


HYDRAULICS. 


[CHAP. Ill 


150 


TABLE III. 


OOJ 


rp s 


OX OVERSHOT WHEELS. 


Number. 

i # 

Whole descent. 

Water expended per minute. 

Turns at the maximum per minute. 

Weight raised at the maximum. 

Power of the whole descent. 

Power of the wheel. 

Effect. 

i 

Ratio of the whole power and effect. 

Ratio of the power of the wheel and 
effect. 

Mean ratio. 

1 . 

inches. 

lbs. 


lbs. 







A 

27 

30 

19 

6 1-2 

810 

720 

556 

10 : 6.9 

10 : 7.7 


2 

27 

56 2-3 

16 1-4 

14 1-2 

1530 

1360 

1060 

10 : 6.9 

10 :7.8 

•- £ 

O CD 

3 

27 

56 2-3 

20 3-4 

12 1-2 

1530 

1360 

1167 

10 :7.6 

10 :8.4 

.. pL 

4 

27 

63 1-3 

20 1-2 

13 1-2 

1710 

1524 

1245 

10 : 7.3 

10 : 8.2 

QO £ 

5 

27 

76 2-3 

21 1-2 

15 1-2 

2070 

1840 

1500 

10 : 7.3 

10 : 8.2 

6 

28 1-2 

73 1-3 

18 3-4 

17 1-2 

2090 

1764 

1476 

10 : 7 

10 : 8.4 

^ O 

7 

28 1-2 

96 2-3 

20 1-4 

20 1-2 

2755 

2320 1868 

10 : 6.8 

10 : 8.1 

QO w 
“ 

8 

30 

90 

20 

19 1-2 

2700 l 2160 1755 

10 : 6.5 

10 :8.1 

©. 

9 

30 

96 2-3 

20 3-4 

20 1-2 

2900|2320 1914 

10 :6.6 

10 : 8.2 


10 

30 

113 1-3 

21 

23 1-2 

3400 

2720 2221 

10 : 6.5 10 : 8.2 

QO 

11 

33 

56 2^ 

20 1-4 

13 1-2 

1870 

1360 

1230 

10 : 6.6 10 : 9. 

o 

112 

33 

106 2-3 

22 1-4 

21 1-2 

3520 

2560 

2153 

10 :6.1 

10 : 8.4 


•13 

33 

146 2-3 

23 

27 1-2 

4840 

3520 

2846 

10 : 5.9 

10 : 8.1 

QO 

Or 

14 

35 

65 

19 3-4 

16 1-2 

2275 

1560 

1466 10 : 6.5 

10 : 9.4 

>— 

o 

15 

35 

120 

21 1-2 

25 1-24200 

2880 2467 10 : 5.9 

10 : 8.6 

00 

bi 

16 

35 

163 1-2 

25 

26 1-2 5728 

3924 2981 10 : 5.2 

10 : 7.6 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 























































































































CHAP. III.] 


HYDRAULICS. 


151 


OBSERVATIONS AND REDUCTIONS FROM THE FOREGOING EXPERI¬ 
MENTS. 

# 

I. Concerning the Ratio between the Power and Effect of 

Overshot Wheels. 

“ The effective power of the water must be reckoned 
upon the whole descent, because it must be raised to that 
height in order to be in a condition of producing the same 
effect a second time. 

The ratios between the power so estimated, and the 
effects at a maximum deduced from the several sets of 
experiments, are exhibited at one view in column 9 of 
table III.; and hence it appears that those ratios differ 
from that of 10 to T.G to that of 10 to 5.2; that is, nearly 
from 4 :3 to 4 :2. In those experiments where the heads 
of water and quantities expended are least, the propor¬ 
tion is nearly as 4 to 3: but where the heads and quan¬ 
tities are greatest, it approaches nearer to that of 4 to 2, 
and by a medium of the whole the ratio is that of 3:2, 
nearly. We have seen before, in our observations upon 
the effects of undershot wheels, that the general ratio of 
the power to the effect, when greatest, was as 3:1. The 
effect, therefore, of overshot wheels , under the same circum¬ 
stances of quantity and fall, is, at a medium , double to that 
of the undershot: and a consequence thereof, that non-elastic 
bodies, when acting by their impulse or collision, communi¬ 
cate only a part of their original power; the other part 
being spent in changing their figure in consequence of 
the stroke.* 

The powers of water computed from the height of the 
wheel only, compared with the effects as in column 10; 
appear to observe a more constant ratio; for if we take 
the medium of each class, which is set down in column 

II, we shall find the extremes to differ no more than 
from the ratio of 10:8.1 to that of 10:8.5 and as the 
second term of the ratio gradually increases from 8.1 to 
8.5 by an increase of head from 3 inches to 11, the ex- 

* These observations of the author agree with the theory, Art. 4 1—42. I may 
add, that non-elastic bodies, when acting by impulse or collision, communicate 
only half of their original power, by the laws of motion. 


152 


HYDRAULICS. 


[CHAP. III. 

cess of 8.5 above 8.1 is to be imputed to the superior im¬ 
pulse of the water at the head of 11 inches, above that 
of 3 inches; so that if we reduce 8.1 to 8, on account of 
the impulse of the 3 inch head, we shall have the ratio 
of the power computed upon the height of the wheel 
only, to the effect at a maximum, as 10:8, or as 5:4, 
nearly. And from the equality of the ratio between 
power and effect, subsisting where the constructions are 
similar, we must infer that the effects as well as the 
powers are as the quantities of water and perpendicu¬ 
lar heights, multiplied together respectively. 

II. Concerning the most proper Height of the Wheel in 
proportion to the ichole Descent. 

“We have already seen, in the preceding observation, 
that the effect of the same quantity of water, descend¬ 
ing through the same perpendicular space, is double, 
when acting by its gravity upon an overshot wheel, to 
what the same produces when acting by its impulse upon 
an undershot. It also appears, that, by increasing the 
head from 3 to 11 inches, that is, the whole descent, from 
27 to 35, or in the ratio of 7 to 9, nearly, the effect is 
advanced no more than in the ratio of 8.1 to 8.4; that is, 
as 7:7.26, and, consequently, the increase of the effect 
is not 1-7tli of the increase of the perpendicular height. 
Hence, it follows, that the higher the wheel is in propor¬ 
tion to the whole descent, the greater will be the effect; 
because it depends less upon the impulse of the head, and 
more upon the gravity of the water in the buckets: and, 
if we consider how obliquely the water issuing from the 
head must strike the buckets, we shall not be at a loss to 
account for the little advantage that arises from the im¬ 
pulse thereof; and shall immediately see of how little con¬ 
sequence this impulse is to the effect of an overshot wheel. 
However, as every thing has its limits, so has this: for 
thus much is desirable, that the water should have some¬ 
what greater velocity than the circumference of the 
wheel, in coming thereon; otherwise the wheel will not 
only be retarded by the buckets striking the water, but 


HYDRAULICS. 


153 


CHAP. HI.] 

thereby dashing a part of it over, so much of the power 
is lost. 

The velocity that the circumference of the wheel 
ought to have being known, the head requisite to give 
the water its proper velocity is easily computed by the 
common rules of hydrostatics, and it will be found much 
less than what is commonly practised. 

III. Concerning the velocity of the Circumference of the 
Wheel in order to produce the greatest effect. 

“ If a body be let fall freely from the surface of the 
head to the bottom of the descent, it will take a certain 
time in falling, and in this case the whole action of gra¬ 
vity is spent in giving the body a certain velocity; but 
if this body in falling be made to act upon some other 
body, so as to produce a mechanical effect, the falling 
body will be retarded; because a part of the action of 
gravity is then spent in producing the effect, and the 
remainder only giving motion to the falling body; and, 
therefore, the slower a .body descends, the greater will 
be the portion of the action of gravity applicable to the 
producing of a mechanical effect. Hence we are led to 
this general rule, that the less the velocity of the wheel, 
the greater will be the effect thereof. A confirmation 
of this doctrine, together with the limits it is subject to 
in practice, may be deduced from the foregoing speci¬ 
men of a set of experiments. 

From these experiments it appears that when the 
wheel made about 20 turns in a minute, the effect was 
nearly upon the greatest; when it made 30 turns, the 
effect was diminished about l-20th part; but that, when 
it made 40, it was diminished about 1-4th: when it 
made less than 181, its motion was irregular; and when 
it was loaded so as not to admit its making 18 turns, 
the wheel was overpowered by its load. 

It is an advantage in practice that the velocity of the 
wdieel should not be diminished farther than what will 
procure some solid advantage in point of power; because, 
as the motion is slower, the buckets must be made larger, 


154 


HYDRAULICS. 


[CHAP. III. 

and the wheel being more loaded with water, the stress 
upon every part of the work will be increased in propor¬ 
tion: the best velocity for practice, therefore, will be 
such as when the wheel here used made about 30 turns 
in a minute; that is, when the velocity of the circum¬ 
ference is a little more than 3 feet in a second. 

Experience confirms that this velocity of 3 feet in a 
second is applicable to the highest overshot wheels as 
well as the lowest; and all other parts of the work being 
properly adapted thereto, will produce very nearly the 
greatest effect possible. However, this also is certain, 
from experience, that high wheels may deviate farther 
from this rule, before they will lose their power, by a 
given aliquot part of the whole, than low ones can be 
‘admitted to do: for a wheel of 24 feet high may move 
at the rate of G feet per second without losing any con¬ 
siderable part of its power; and, on the other hand, 1 
have seen a wheel of 33 feet high that has moved very 
steadily and well, with a velocity but little exceeding 
2 feet.”* 

[Mr. Smeaton has also made a model of a wind-mill, 
and a complete set of experiments on the power and ef¬ 
fect of the wind, acting on wind-mill sails of different 
constructions. But as the accounts thereof are quite 
too long for the compass of my work, I therefore extract 
little more than a few of the principal maxims deduced 
from his experiments, which, I think, may not only be 
of use to those who are concerned in building wind-mills, 
but may, also, serve to confirm some principles deduced 
from his experiments on water-mills.] 

* Probably this wheel was working a forge or furnace bellows, which have 
deceived many by their slow regular motion. 


CHAP. III.] 


HYDRAULICS. 


155 


PART III. 


ARTICLE 69. 


OF THE CONSTRUCTION AND EFFECTS OF WIND-MILL SAILS . 4 

“In trying experiments on wind-mill sails, the wind 
itself is too uncertain to answer the purpose; we must, 
therefore, have recourse to artificial wind. 

This may be done two ways; either by causing the 
air to move against the machine, or the machine to 
move against the air. To cause the air to move against 
the machine in a sufficient column, with steadiness and 
the requisite velocity, is not easily put in practice: to 
carry the machine forward in a right line against the 
air, would require a larger room than I could conveni¬ 
ently meet with. What I found most practicable, there¬ 
fore, was to carry the axis whereon the sails were to be 
fixed progressively round in the circumference of a large 
circle. Upon this idea the machine was constructed.]* 


Specimen of a set of Experiments. 


Radius of the sails, - 

Length of do. in cloth, - 
Breadth of do. - 

{ Angle at the extremity, 

Do. at the greatest inclination, 

20 turns of the sails raised the weight, 
Velocity of the centre of the sails in the cir¬ 
cumference of the great circle in a second, 
in which the machine was carried round, 
Continuance of the experiment, 


21 inches. 
18 
5.6 

10 degs. 
25 

11.3 inch. 
j-G feet. 

52 seconds. 


* Read May 31st and June 14th, 1759, in the Philosophical Society of London. 

11 decline giving any description or draught of this machine, as I have not 
room; but I may say that it was constructed so as to wind up a weight, (as did 
the other model,) in order to find the effect of the power. I also insert a speci¬ 
men of a set of experiments, which I fear will not be well understood for want 
of a full explanation of the machine. 

f In the following experiments, the angle of the sails is accounted from the 
plane of their motion; that is, when they stand at right angles to the axis, their 
angle is denoted ° deg.; this notation being agreeable to the language of practi¬ 
tioners, who call the angle so denoted the weather of the sail; which they deno¬ 
minate greater or less, according to the quantity of the angle. 


156 

HYDRAULICS. 

[chap. III. 

No. 

Weight in the scale. 

Turns. 

Product. 

1 

0 lbs. 

108 

0 

2 

6 

85 

510 

o 

O 

61 

81 

5261 

4 

t"T 

/ 

78 

546 

5 

71 

73 

5471 maxim. 

6 

8 

65 

520 

7 

9 

0 

0 

The product was found 

by simply 

multiplying the 


weight in the scale by the number of turns. 

By this set of experiments it appears that the maxi¬ 
mum velocity is 2-3ds of the greatest velocity, and that 
the ratio of the greatest load to that of the maximum 
is as 9 to 7.5, but by adding the weight of the scale and 
friction to the load, the ratio turns out to be as 10 : 8.4, 
or 5 to 4, nearly. The following table is the result of 
19 similar sets of experiments. 

By the following table it appears that the most gene¬ 
ral ratio between the velocity of the sails unloaded and 
when loaded to a maximum, is 3 to 2, nearly. 

And the ratio between the greatest load and the load 
at a maximum (taking such experiments where the sails 
answered best,) is at a medium about as G to 5, nearly. 

And that the kind of sails used in the 15tli and 16th 
experiments are best of all, because they produce the 
greatest effect or product, in proportion to tlieir quantity 
of surface, as appears in column 12. 


CHAP. III.] 


HYDRAULICS 


157 


TABLE IY. 

Containing nineteen sets of experiments on wind-mill sails of various 
structures, positions and quantities of surface. 


The kind of sails made use of. 

Number. 

Angle at the extremities. 

Greatest angle. 

Turns of the sails, unloaded. 

Turns at a maximum. 

Load at a maximum. 

Greatest load. 

Product. 

Quantity of surface. 

Ratio of the greatest velocity to the 
velocity at a maximum. 

Ratio of the greatest load to the load 
at a maximum. 

Ratio of the surface to the pro¬ 
duct. 



Deg. 

Deg. 



lbs. 

lbs. 


sq.in. 




I. 

1 

35° 

35° 

66 

42 

7.56 

12.59 

318 

404 

10:7 

10:6 

10: 7. 9 


2 

12 

12 


70 

6.3 

7.56 

441 

404 


10:8.3 

10:10. 1 

II. 

3 

15 

15 

105 

69 

6.72 

8.12 

464 

404 

10:6.6 

10:8.3 

10:10.15 


4 

18 

18 

96 

66 

7.0 

9.81 

462 

404 

10:7 

10:7.1 

10:10.15 


5 

9 

26.5 


66 

7.0 


462 

404 



10:11. 4 

III. 

C 

12 

29.5 


70.5 

7.35 

• 

518 

404 



10:12. 8 


7 

15 

32.5 


63.5 

8.3 


527 

404 



10:13. 0 


8 

0 

15 

120 

93 

4.75 

5.31 

442 

404 

10:7.7 

10:8.9 

10:11. 0 


9 

3 

18 

120 

79 

7.0 

8.12 

553 

404 

10:6.6 

10:8.6 

10:13. 7 


10 

5 

20 


78 

7.5 

8.12 

585 

404 


10:9.2 

10:14. 5 

IV. 

11 

7.5 

22.5 

113 

77 

8.3 

9.81 

639 

404 

10:6.8 

10:8.5 

10:15. 8 


12 

10 

25 

108 

73 

8.69 

10.37 

634 

404 

10:6.8 

10:8.4 

10:15. 7 


13 

12 

27 

100 

66 

8.41 

10.94 

580 

404 

10:6.6 

10:7.7 

10:14. 4 


14 

7.5 

22.5 

123 

75 

10.65 

12.59 

799 

505 

10:6.1 

10:8.5 

10:15. 8 


15 

10 

25 

117 

74 

11.08 

13.69 

820 

505 

10:6.3 

10:8.1 

10:16. 2 

Y. 

16 

12 

27 

114 

66 

12.09 

14.23 

799 

505 

10:5.8 

10:8.4 

10:15. 8 


17 

15 

30 

96 

63 

12.09 

14.78 

762 

505 

10:6.6 

10:8.2 

10:15. 1 


18 

12 

22 

105 

64.5 

16.42 

27.87 

1059 

854 

10:6.1 

10:5.9 

10:12. 4 

VI. 

19 

12 

22 

99 

64.5 

18.06 


1165 

1146 

10:5.9 


10:10. 1 


1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 


I. Plain sails at an angle of 55 degrees. 

IT. Plain sails weathered according to common practice. 

III. Weathered according to Maclaurin’s theorem. 

1Y. Weathered in the Dutch manner, tried in various positions. 

V. Weathered in the Dutch manner, but enlarged towards the extremities. 
VI. Eight sails, being sectors of ellipses in their best position. 



















































































































158 


[chap. III. 


HYDRAULICS. 

» 


TABLE V. 


Containing the result of six sets of experiments, made for determining the dif¬ 
ference of effect according to the different velocity of the wind. 


Ratio of the greatest load to the load at a 
maximum. 


CO T-l 

GO 05 

O O 

r-l rH 


m 

00 oo 

o o 

rH rH 

i 

rH 

Ratio of the greatest velocity to the ve¬ 
locity at a maximum. 


05 05 

CO irf 
• • • 

o o 

rH r-H 


t- O i 

CD CD 

O O 

r-H rH 

co 

1 

Ratio of the two products. 


CO 

Oi 

© 

r-H 

00 

<N 

o 

10:26 

C* | 

Product of the lesser load and greater 
velocity. 


m 

o 

00 

(N 

CO 

oo 

in 

05 

1 

1 

rH 

Turns of the sails therewith. 


o 

00 

rH 

o 

00 

hH 

SP 

o 

o 

rH 

Maximum load for half the velocity. 


f" 

Tf 

• 

Z9'l 

CO 

o 

in 

05 

Product. 


m co 

05 O 

DJ O 
<N 

O 00 

O 

CO <N 

O) 

r- 
O H 

00 O 
oi 

00 I 

Greatest load. 

in 

r£ 

5. 37 
18. 06 


5. 87 
21.34 


Load at the maximum. 

£ 

4. 47 
16. 42 

4. 62 
17.52 

00 rH 

O CO 

in od 

rH 

— 

CD j 

Turns of the sails at a maximum. 


CO OJ 

CD OJ 

T—1 

m o 

CO CO 

rH 

61 

110 

1 

Turns of the sails unloaded. 


CD t— 

05 © 


rH 00 

05 i> 

T-H 

•rH 

Velocity of the wind in a second. 

d 

• r-H 

• 

rf 05 

00 

•in 

05 

Tt< 00 

•HOI 

rr 05 

■H 00 

CO 

Angle at the extremity. 

degr. 

m m 

in m 

• • 

O © 

rH r-H 

O* 1 

Number. 


rH Oi 

CO r 

m co 



N. B.—The sails were of the same size and kind as those of Nos. 10, 11, and 
12, Table IV. Continuance of the experiment one minute. 





















































































































CHAP. III.] 


HYDRAULICS. 


159 


Concerning the effects of sails according to the different 

velocity of the wind. 

u From the foregoing table the following maxims are 
deduced. 

Maxim I. The velocity of wind-mill sails, whether un¬ 
loaded or loaded, so as to produce a maximum, is near¬ 
ly as the velocity of the wind, their shape and position 
being the same. 

This appears by comparing the respective numbers 
of columns 4 and 5, table V., wherein those numbers, 2, 
4 and 6, ought to be double of No. 1, 3 and 5, and are 
as nearly so as can be expected by the experiments. 

Maxim II. The load at the maximum is nearly, but 
somewhat less than, as the square of the velocity of the 
wind, the shape and position of the sails being the same. 

This appears by comparing No. 2,4 and 6, in column 
6, with 1, 3 and 5, wherein the former ought to be 
quadruple of the latter, (as the velocity is double,) and 
are as nearly so as can be expected. 

Maxim III. The effects of the same sails at a maxi¬ 
mum are nearly, but somewhat less than, as the cubes 
of the velocity of the wind.* 

It has been shown, maxim I., that the velocity of sails 
at a maximum is nearly as the velocity of the wind; 
and by maxim II., that the load at the maximum is 
nearly as the square of the same velocity. If those two 
maxims would hold precisely, it would be a consequence 
that the effect would be in a triplicate ratio thereof. 
How this agrees with experiment will appear by com¬ 
paring the products in column 8, wherein those of No. 
2, 4 and 6, (the velocity of the wind being double,) 
ought to be octuple of those of No. 1, 3 and 5, and are 
nearly so. 

Maxim IV. The load of the same sails at the maxi¬ 
mum is nearly as the squares of, and their effects as the 
cubes of, their number of turns in a given time. 


* This confirms the 7th law of spouting fluids. 


160 HYDRAULICS. [CHAP. III. 

This maxim may be esteemed a consequence of the 
three preceding ones.” 

These 4 maxims agree with and confirm the 4 max¬ 
ims concerning the effects of spouting fluids acting on 
undershot mills; and, I think, sufficiently confirm as a 
law of motion, that the effect produced, if not the in¬ 
stant momentum of a body in motion, is as the square of 
its velocity, as asserted by the Dutch and Italian philo¬ 
sophers. Smeaton says that by several trials in large, 
he has found the following angles to answer as well as 

any:— 

“ The radius is supposed to be divided into 6 parts; 
and 1-6th, reckoning from the centre is called 1, the 


extremity being denoted 6. 

No. Angle with the axis. Angle with the plane of motion. 

1 

72° 

18° 

2 

71 

19 

o 

O 

72 

18 middle. 

4 

74 

16 

5 

77* 

121 

6 

83 

7 extremity.” 

He seems 

• . • 

to prefer the sails being 

largest at the ex 


tremities. 


END OF PART FIRST. 


THE 


YOUNG MILL-WEIGHT’S GUIDE. 


pwA iju §m\\t 


INTRODUCTION. 

What has been said in the first part was meant to 
establish theories and to furnish easy rules. In this 
part I mean to show their practical application in as 
concise a manner as possible, referring only to the ar¬ 
ticles in the first part, where the reasons and demon¬ 
strations are given. 

This part is particularly intended for the help of 
young and practical mill-wrights, whose time will not 
admit of a full investigation of those principles and the¬ 
ories which have been laid down: I shall, therefore, en¬ 
deavour to reduce the substance of all that has been 
said to a few tables, rules, and short directions, which, if 
found to agree with experience, will be sufficient for the 
practitioner. 


CHAPTER IV. 

OF THE DIFFERENT KINDS OF MILLS. 

ARTICLE 70. 

OF UNDERSHOT MILLS. 

Undershot wheels move by the percussion or stroke of 
the water, and are only half as powerful as other wheels 

11 




162 OF UNDERSHOT MILLS. [CItAP. IV. 

that are moved by the gravity of the water. See Art. 9. 
Therefore, this construction ought not to be adopted 
except where there is but little fall, or great plenty ot 
water. The undershot wheel, and all others that move 
by percussion, should move with a velocity nearly equal 
to two-thirds of the velocity of the water. See Art. 42, 
Fig. 28, Plate IV., represents this construction. 

For a rule for finding the velocity of the water under 
any given head, see Art. 51. Upon the principles, and 
by the rule, given in that article, is formed the following 
table of the velocity of spouting water, under different 
heads, from one to twenty-five feet high above the centre 
of the issue; to which is added the velocity of the wheel 
suitable thereto, and the number of revolutions a wheel 
of fifteen feet diameter (which I esteem a good size) will 
revolve in a minute; also the number of cogs and rounds 
in the wheels, both for double and single gears, so as 
to produce about ninety-seven or one hundred revolu¬ 
tions per minute for a five feet stone, which I think a 
good motion and size for a mill stone, grinding for mer¬ 
chantable flour. 

That the reader may fully understand how the fol¬ 
lowing table is calculated, let him observe, 

1. That by Art. 42, the velocity of the wheel must be 
just 577 thousandth parts of the velocity of the water; 
therefore, if the velocity of the water, per second, be mul¬ 
tiplied by .577, the product will be the maximum velo¬ 
city of the wheel, or velocity that will produce the great¬ 
est effect, which is the third column in the table. 

2. The velocity of the wheel per second, multiplied 
by 60, produces the distance the circumference moves 
per minute, which divided by 47.1 feet, the circumfe¬ 
rence of a 15 feet wheel, gives the number of revolutions 
of the wheel per minute, which is the fourth column. 

3. That, by Art. 20 and 74, the number of revolutions 
of the wheel per minute, multiplied by the number of 
cogs in all the driving wheels, successively, and that 
product divided by the product of the number of cogs 
in all the leading wheels, multiplied successively, the 
quotient is the number of revolutions of the stones per 


CHAP. IV.] OF UNDERSHOT MILLS. 163 

minute, which is found in the ninth and twelfth co¬ 
lumns. 

4. The cuboclis of power required to drive the stone 
being, by Art. 61, equal to 111.78 cubochs per second, 
which divided by half the head of water, added to all 
the fall, (if any,) being the virtual or effective head by 
Art. 61, gives the quantity of water, in cubic feet, re¬ 
quired per second, which is found in the thirteenth co¬ 
lumn. 

5. The quantity required, divided by the velocity with 
which it is to issue, gives the area of the aperture of 
the gate, and is shown in the fourteenth column. 

6. The quantity required, divided by the velocity 
proper for the water to move along the canal, gives the 
area of the section of the canal, as in the fifteenth co¬ 
lumn. 

7. Having obtained their areas, it is easy, by Art. 65, 
to determine the width and depth, which may be varied 
to suit other circumstances. 


164 


OF UNDERSHOT MILLS 


[CHAP. IV 


TIIE MILL-WEIGHT'S TABLE 

» 70 R 

UNDERSHOT MILLS, 

Calculated for a water-wheel of fifteen feet, and sto7ies of 

five feet diameter. 


Head of water above the point of im¬ 
pact. 

Velocity of the water per second at the 
point of impact. 

Velocity of the wheel per second, loaded 
at the maximum. 

Number of revolutions of the wheel of 
15 feet diameter, per minute. 

No. of cogs in the master cog-wheel. 

Rounds in the wallower. 

Cogs in the counter-cog-wheel. 

Rounds in the trundle. 

Revolutions of the stone per minute. 

Cogs in the cog-wheel for single gear. 

Rounds in the trundle. 

Revolutions of the stone per minute. 

Cubic feet of water'required per second 
to drive a 5 feet stone 97 revolutions 
per minute. 

Area of the gate to vent the water, or ra¬ 
ther of a section of the column of wa¬ 
ter at a place of impact. 

Area of a section of the canal sufficient 
to bring on the water with 1.5 feet ve¬ 
locity. 

feet. 

feet. 

feet. 









cub. ft. 

sup. ft. 

sup. ft. 

1 

8.1 

4.67 

5.94 

112 

22 54 

16 

101.6 




223.5 

27.5 

149. 

2 

11.4 

6.57 

8.36 

962351 

19 

99 




111.78 


9.8 

74.5 

3 

14. 

8.07 

10.28 

88*25 54 

19 

100.5 




74.52 


4.6 

43. 

4 

10.2 

9.34 

11.19 

78 23 48 

20 

97 




55.89 


3.45 

37.26 

5 

18. 

10.38 

13.22 

6624 

48 

18 

97 

112115 

98.66 

44.7 


2.48 

29.8 

1 6 

19.84 

11.44 

14.6 

6624 

48 

20 

96.2 

112 

17 

96.2 

37.26 


1.9 

24.84 

7 

21.43 

12.36 

15.74 

66 25 

44 

19 

96.2 

104 

17 

96.2 

31.9 


1.48 

21.26 

8 

22.8 

13.15 

10.75 

66 

25 

44 

20 

97.2 

96 

16 

100. 

27.94 


1.22 

18.6 

9 

24.3 

14.02 

17.86 

66 

26 

42 

19 

100.2 

96 

17 

100.8 

24.84 


1.02 

16.56 

10 

25.54 

14.73 

18.78 

60 

25 

4-1 

20 

99 

96 

lh 

100. 

22.89 


.9 

15.26 

11 

26.73 

15.42 

19.7 

60 

26 

44 

20 

100 

96 

19 

99.5 

20.32 


.76 

13.54 

12 

28. 

16.10 

20.5 

60 

27 

44 

20 

100 

9G 

-.0 

98.4 

18.63 


.66 

12.42 

13 

29.10 

16.82 

21.42 

60 

27 

42 

20 

99.8 

96 

21 

102.6 

16.27 


.56 

10.8 

14 

30.2 

17.42 

22.19 

| 60 

28 

42 

20 

99 

88 

20 

97.63 

15.94 


.53 

10.6 

15 

31.34 

18.08 

23.03 

60 

29 

42 

20 

99 

88 

21 

96.5 

14.9 


.47 

9.93 

10 

32.4 

18.69 

23.8 






88 

21 

99.7 

13.97 


.43 

9.31 

17 

33.32 

19.22 

24.48 






84 

21 

97.9 

13.14 


.39 

8.76 

18 

34.34 

19.81 

25.23 






80 

21 

96.1 

12.42 


.36 

8.28 

19 

35.18 

20.29 

25.82 


» 




80 

21 

98.3 

11.76 


.33 

7.84 

20 

30.2 

20.88 

26.6 






78 

21 

98.3 

11.17 


.3 

7.4 

21 

37.11 

21.41 

27.26 






78 

2 

97. 

10.64 


.29 

7.1 

22 

37.98 

21.86 

27.84 






78 

22 

98.6 

10.16 


.26 

6.77 

23 

38.79 

22.38 

28.5 






72 

21 

97.7 

9.72 


.25 

6.48 

24 

39.69 

22.90 

29.17 






66 20 

96.2 

9.32 


.23 

6.21 

25 

40.5 

23.36 

29.75 






60 

18 

99. 

8.94 


.22 

5.96 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 
























































































CHAP. IV.] OF UNDERSHOT' MILLS. 165 

It must be observed, that five feet fall is the least that 
a single gear can be built on, to keep the cog-wheel clear 
of the water, and give the stone sufficient motion. 

Although double gear is calculated to fifteen feet fall, 
yet I do not recommend them above ten feet, unless for 
some particular convenience, such as for two pairs of 
stones to one wheel, &c., &c. The number of cogs in 
the wheels is even, and is thus suited to eight, six, or 
four arms, so as not to pass through any of them, this 
being the common practice; but when the motion cannot 
be obtained without a trundle that will cause the same 
cogs and rounds to meet too often, such as 16 into 96, 
which will meet every revolution of the cog-wheel, or 
18 to 96, which will meet every third revolution, I ad¬ 
vise the putting in either of one more or one less, as 
may best suit the motion, which will cause them to 
change oftener. See Art. 82. 

It should be recollected that the friction at the aper¬ 
ture of the gate will greatly diminish both the velocity 
and power of the water, where the head is great, if the 
gate be made of the usual form, that is, wide and shal¬ 
low. Where the head is great, the friction will be great. 
See Art. 55therefore, the wheel must be narrow, and 
the aperture of the gate of a square form, in order to 
avoid the friction and loss in a wide wheel, especially 
if it do not run very closely to the sheeting. 

Use of the Table . 

Having levelled your mill-seat carefully, and finding 
such fall and quantity of water as determines you to 
make choice of an undershot wheel; for instance, sup¬ 
pose 6 feet fall, and about 45 cubic feet of water per se¬ 
cond, which you may find in the way directed in Art. 53; 
cast off about one foot for fall in the tail-race below the 
bottom of the wheel, if subject to back-water, which leaves 
you 5 feet head; then look for 5 feet head in the first 
column of the table, and against it are all the calculations 
for a 15 feet water-wheel, and 5 feet stones; in the thir¬ 
teenth column you have 44.7 cubic feet of water, which 
shows you have enough for a pair of five feet stones; and 


1G6 OF UNDERSHOT MILLS. [CHAP. IV. 

the velocity of the water will be 18 feet per second, the 
velocity of the wheel 10.38 feet per second, and it will 
revolve 13.22 times per minute. If you choose double 
gear, then 06 cogs in the master cog-wheel, 24 rounds 
in the wallower, 48 cogs in the counter cog-wheel, and 
18 rounds in the trundle, will give the stone 97 revolu¬ 
tions in a minute; if single gear, 112 cogs and 15 rounds 
give 98.66 revolutions in a minute; it will require 44.7 
cubic feet of water per second; the size of the gate must 
be 2.48 feet; which will be about 4 feet wide, and .62 
feet, or about 71 inches deep: the size of the canal must 
be 29.8 feet; that is, about 3 feet deep, and 9.93 or 
nearly 10 feet wide. If you choose single gear, you must 
make your water-wlieel much smaller, say 7~, the half 
of 15 feet, then the cog-wheel must have half the number 
of cogs, the trundle head the same, the spindle will be 
longer, and the husk lower; the mill will then be full 
as good as with double gear: in the case supposed, how¬ 
ever, a cog-wheel of 66 cogs would not answer, because 
it would reach the water; but where the head is ten or 
twelve feet, it will do very well. 

If you choose stones, or water-wheels, of other sizes, 
it will be easy, by similar rules, to proportion the whole 
to suit, seeing you have the velocity of the periphery 
of a wheel of any size.* 


* One advantage large wheels have over small ones is, that they cast off the 
back-water much better. The buckets of the low w’heel will lift the w r ater 
much more than those of the high wheel; because the nearer the water rises to 
the centre of the wheel, the nearer the buckets approach the horizontal or lifting 
position. 

To make a wheel cast off back-water, some mill-wrights fix the sheeting below 
the wheel, with joints and hinges, so that the end down stream can be raised so 
as to shoot the water, as it leaves the wheel, on the surface of the back-water, 
and thus roll it from the wheel: it is thought that it will drive off the back-water 
much better. 

Plate IV. fig. 28, shows an undershot wheel. Some mill-wrights prefer to 
slant the forebay under the wheel, as in the figure, that the gate may be drawn 
near the floats; because they think that the water acts with more power near 
the gate, than at a distance; which appears to be the case when we consider, 
that the nearer we approach the gate, the nearer the column of water approaches 
to what is called a perfectly definite quantity. See Art. 59. 

Others, again, say, that it acquires equal power of descending the shute. (It 
will certainly acquire equal velocity, abating only for the friction of the shute 
and the air.) When the shute has a considerable descent, the greater the dis¬ 
tance from the gate, the greater the velocity and power of the water; but where 
the descent of the shute is not sufficient to overcome the friction of the air, &c., 


CHAP. IV.] 


OF TUB MILLS. 


1G7 


Observations on the table. 

1. The table is calculated for an undershot wheel con¬ 
structed, and the water shot on, as in Plate IV., fig. 28. 
The head is counted from the point of impact I., and the 
motion of the wheel at a maximum, about .58 of the ve¬ 
locity of the water; but when there is plenty of water 
and great head, the wheel will run best at about .GG or 
two-thirds of the velocity of the water; therefore, the 

. stones will incline to run faster than in the table, in the 
ratio of 58 to GG, nearly; for which reason I have set 
the motion of 5 feet stones under 100 revolutions in a 
minute, which is slower than common practice: they 
will incline to run between 9G and 110 revolutions. 

2. I have taken half of the whole head above the 
point of impact for the virtual or effective head by Art. 
53, which I apprehend will be too little in very low 
heads, and, perhaps, too much in high ones. As the 
principle of non-elasticity does not seem to operate 
against the power so much in low as in high heads, 
therefore, if the head be only 1 foot, it may not require 
223.5 cubic feet of water per second, and if 20 feet, may 
require more than 11.17 cubic feet of water per second, 
the quantities given in the table. 


ARTICLE 71. 

OF TUB MILLS. 

A tub mill has a horizontal water-wheel that is acted 
on by the percussion of the water altogether; the shaft is 

then the nearer the gate, the greater the velocity and power of the water; which 
argues in favour of drawing the gate near the iloats. Yet, where the fall is 
great, or water plenty, and the expense of a deep penstock considerable, the 
small difference of power is not worth the expense of thus obtaining it. In these 
cases, it is best to have a shallow penstock, and a long shute to convey the water 
down to the wheel, drawing the gate at the top of the shute : this is frequently 
done to save expense in building saw-mills, with flutter-wheels, which are small 
undershot wheels, fixed on a crank shaft, and made so small as to obtain a suffi¬ 
cient number of strokes of the saw in a minute, say about 120. This wheel is 
to be of such a size as is calculated to suit the velocity of the water at the point 
of impact, so as to make that number of revolutions (120) in a minute. 

Thomas Lllicott’s method of shooting the water on an undershot-wheel, where 
the fall is great, is shown in Plate 13, fig. 0. 



168 OF TUB MILLS. [CIIAP. IY. 

vertical, carrying tlie stone on the top of it, and serves 
in place of a spindle; tlie lower end of this shaft is set 
in a step fixed in a bridge-tree, by which the stone is 
raised and lowered, as by the bridge-tree of other mills; 
the water is shot on the upper side of the wheel, in the 
direction of a tangent with its circumference. See fig. 
29, Plate IV., which is a top view of the tub-wheel, and 
fig. 30, which is a side view of it, with the stone on the 
top of the shaft, bridge-tree, &c. The wheel runs in a 
hoop, like a mill-stone hoop, projecting so far above the 
wheel as to prevent the water from shooting over the 
wheel, and whirls it about until it strikes the buckets, 
because the water is shot on in a deep, narrow, column 
9 inches wide, and 18 inches deep, to drive a 5 feet stone, 
with 8 feet head—the whole of this column cannot en¬ 
ter the buckets until a part has passed half way round 
the wheel, so that there are always nearly half the buck¬ 
ets struck at once; the buckets are set obliquely that 
the water may strike them at right angles. See Plate 
IV., fig. 30. As soon as it strikes, it escapes under the 
wheel in every direction, as in fig. 29.* 


* Note. That in Plate IV. fig. 30, I have allowed the gate to be drawn in¬ 
side of the penstock, and not in the shute near the wheel, as is the common 
practice; because the water will leak out much alongside of the gate, if drawn 
in the shute. But here we must consider that the gate must always be full 
drawn, and the quantity of water regulated by a regulator in the shute near the 
wheel; so that the shute will be perfectly full, and pressed w r ith the whole 
weight of the head, else a great part of the power may be lost. 

To show this more plainly, suppose the long shute A, from the high head 
(shown by dotted lines) of the undershot mill, fig. 28, be made tight by being 
covered at top, then, if we draw the gate A, but not fully, and if the shute at 
bottom be large enough to vent all the water that issues through the gate when 
the shute is full to A, ihen it cannot fill higher than A: therefore, all that part 
of the head above A is lost, it being of no other service than to supply the shute, 
and keep it full to A, and the head from A to the wheel, is all that acts on the 
wheel. 

Again, when we shut the gate, the shute cannot run empty, because it would 
leave a vacuum in the head of the shute at A; therefore, the pressure of the at¬ 
mosphere resists the running out of the water from the shute, and whatever head 
of water is in the shute when the gate is shut, will balance its weight of the 
pressure of the atmosphere, and prevent it from acting on the lower side of the 
gate, which will cause it to be very hard to draw. For, suppose 11 feet head 
of water to be in the shute when the gate was shut, its pressure is equal to about 
5 lbs. per square inch; then, if the gate be 48 by 6 inches, which is equal to 
288 inches, this multiplied by 5, is equal to 1440 lbs., the additional pressure 
on the gate. 

Again, if the gate be full drawn, and the shute be not much larger at the up¬ 
per than the lower end, these defects will cause much loss of power. To remedy 
all this, put the gate H at the bottom of the shute, to regulate the quantity of 
water by, and make a valve at A to shut on the inside of the shute, like the 
valve of a pair of bellows, which will close when the gate A is drawn, and open 


OF TUB MILLS. 


169 


CHAP. IY.] 

The disadvantage of these wheels are, 

1. Under the best construction the water does not act 
to advantage on them; and it is, in general, necessary to 
make them so small, in order to give velocity to the stone, 
that the buckets take up a third part of their diameter. 

2. The water acts with less power than on undershot 
wheels, as it is less confined at the time of striking the 
wheel, and its non-elastic principle operates more fully. 

3. If the head be low, it is with difficulty we can put 
a sufficient quantity of water to act on them so as to 
drive them with sufficient power; I therefore advise to 
let the water strike on them in two places, as in Plate 
IV., fig. 29; the apertures need then only be about 6 
by 13 inches each, instead of 9 by 18; they will then 
ojierate to more advantage, as nearly all the buckets 
will be acted on at once. 

Their advantages are, 

Their exceeding simplicity and cheapness, having no 
cogs nor rounds to be kept in repair, their wearing parts 
are few, and have but little friction; the step-gudgeon 
runs under water, therefore, if well fixed, it will not get 
out of order in a long time; they will move with suffi¬ 
cient velocity and power with 9 or 10 feet total fall, if 
there be plenty of water; and if they be well fixed, they 
will not require much more water than undershot 
wheels; they are, therefore, preferable in all seats which 
have a surplus of water, and above 8 feet fall. 

In order that the reader may fully understand how 
the following table for tub-mills is calculated, let him 
consider, 

1. That the tub-wheel moves altogether by percussion, 
the water flying clear of the wheel the instant it strikes, 
and that it is better, (by Art. 70,) for such wheels to move 
faster than the calculated maximum velocity: therefore, 
instead of .577, we will allow them to move .66 velocity 
of the water; then multiplying the velocity of the water 


when the gate shuts, and let air into the shute; this plan will do better for saw¬ 
mills with flutter-wheels, or tub-mills, than long open shutes, as by it we avoid 
the friction of the shute and the resistance of the air. 

To understand what is here said, the reader must be acquainted with the theory 
of the pressure of the atmosphere, vacuums, &c. See these subjects touched on 
in Art. 5G. 


170 


OF TUB MILLS. 


[CHAP. IV. 

by .GG, gives the velocity of the wheel at the centre of 
the buckets, which constitutes the third column in the 
table. 

2. The velocity of the wheel per second multiplied by 
GO, and divided by the number of revolutions the stone 
is to make in a minute, gives the circumference of the 
wheel at the centre of the buckets; which circumfe¬ 
rence, multiplied by 7, and divided by 22, gives the di¬ 
ameter from the centre of the buckets, to produce the 
number of revolutions required, which are contained 
in the 4th, 5th, Gtli and 7th columns. 

3. The cubochs of power required by Art. G3, to drive 
the stone, divided by half the head, give the cubic feet 
of water required to produce said power, which are 
found in the 8th and 10th columns. 

4. The cubic feet of water, divided by the velocity, 
will give the sum of the apertures of the gates, which 
are shown in the 9th and lltli columns. 

5. The cubic feet of water, divided by 1.5 feet, the ve¬ 
locity of the water in the canal, gives the area of a sec¬ 
tion of the canal, which is shown in the 12th and 13th 
columns. 

6. For the quantity of water, aperture of gate, and 
size of canal, for 5 feet stones, see table for undershot 
mills, in Art. 70. 


CHAP. IV.] 


OF TUB MILLS 


171 


TIIE MILL-WRIGIIT’S TABLE 

FOR 

TUB MILLS. 






























































































172 


OF BREAST MILLS. 


[cnAP. IV. 


Use of the Table for Tub Mills. 

Having levelled your mill-seat, and found that you 
have above 8 feet fall, and plenty of water, and wishing 
to build a mill on the simplest, cheapest, and best con¬ 
struction to suit your seat, you will, of course, make 
choice of a tub mill. 

Cast off 1 foot for fall in the tail-race, below the bot¬ 
tom of the wheel, if it be subject to back water, and 9 
inches for the wheel; then suppose you have 9 feet left 
for head above the wheel; look in the table against 9 
feet head, and you have all the calculations necessary 
for 4, 5, 6, and 7 feet stones, the quantity of water re¬ 
quired to drive them, the sum of the areas of the aper¬ 
tures, and the areas of the canals. 

If you choose stones of any other size, you can easily 
proportion the parts to suit, by the rules by which the 
table is calculated. 

Let it be recollected, however, that it is a very common 
error, to build tub mills in situations where they must 
fail during a dry season. They arc suited to those places 
only where water runs to waste during the whole year. 
There are hundreds of such mills in the United States 
which are useless at the season when they are most 
needed, whilst a well-constructed overshot, breast, or 
pitch-back wheel, might be kept constantly running. 


i 

ARTICLE 72. 

OF BREAST MILLS. 

Breast wheels, which have the water shut on them in 
a tangential direction, are acted on by the principles both 
of percussion and of gravity; all that part above the point 
of impact, called head, acts by percussion; and all that 
part below said point, called fall, acts by gravity. 

We are obliged, in this structure of breast mills, to 
use more head than will act to advantage; because we 
cannot strike the water on the wheel, in a true tangen- 



CHAP. IV.] OF BREAST MILLS. 173 

tial direction, higher than I. the point of impact, as 
shown in Plate IY., fig. 31, which is a breast wheel with 
12 feet perpendicular descent, 6.5 feet of which are above 
the point I., as head, and 5.5 feet below, as fall. The 
upper end of the sliute that carries the water down to the 
wheel, must project some inches above the point of the 
gate when full drawn, otherwise the water will strike 
towards the centre of the wheel; and it must not project 
too high, or else the water in the penstock will not come 
fast enough into the shute when the head sinks a little. 
The bottom of the penstock is a little below the top end 
of the shute, to leave room for stones and gravel to set¬ 
tle, and prevent them from getting into the gate. 

We might lay the water on higher, by setting the top 
of the penstock close to the wheel, and using a sliding 
gate at bottom, as shown by the dotted lines; but this is 
not approved of in practice. See Ellicott’s mode, Plate 
XV., fig. 1. 

But if the water in the penstock be nearly as high as 
the wheel, it may be carried over; as shown by the upper 
dotted lines, and shot on backwards, making that part 
next the wheel the shute to guide the water into the 
wheel, and the gate very narrow or shallow, allowing the 
water to run over the top of it when drawn: by this 
method (called pitch-back) the head may be reduced to 
the same as it is for an overshot wheel; and then the 
motion of the circumference of the wheel will be equal 
to the motion of an overshot wheel, whose diameter is 
equal to the fall below the point of impact, and their 
powers will be equal. 

This structure of a wheel, Plate IY., fig. 31,1 view as 
a good one for the following reasons, namely:— 

1. The buckets, or floats, receive the percussion of 
the water at right angles, which is the best direction 
possible. 

2. It prevents the water from flying towards the cen¬ 
tre of the wheel without reacting against the bottom of 
the buckets, and retains it in the wheel, to act by its 
gravity in its descent, after the stroke. 

3. It admits air, and discharges the water freely, with- 


174 


OF BREAST MILLS. 


[CHAP. IV. 

out lifting it at bottom; and this is an important advan¬ 
tage, because, if the buckets of a wheel be tight, and the 
wheel wade a little in back-water, they will lift the wa¬ 
ter to a considerable distance as they empty; the pres¬ 
sure of the atmosphere then prevents the water from 
leaving the buckets freely, and it requires a great force 
to lift them out of the water with the velocity of the 
wheel; this may be proved by dipping a common water- 
bucket into the water, and lifting it out, bottom up, with 
a quick motion; you have to lift not only the water in the 
bucket, but it appears to suck much more up after it; 
which is the effect of the pressure of the atmosphere. 
See Art. 56. This shows the necessity of air-holes to 
let air into the buckets, that the w r ater may have liberty 
to escape freely. 

Its disadvantages are, 

1. It loses much water, if it be not kept closely to the 
sheeting. And, 

2. It requires too great a part of the total fall to be 
used as head, which is a loss of power, one foot fall 
being equal in power to two feet head. 

Plate IV., fig. 32, is a draught, showing the position of 
the shute for striking the water on a wheel in a tangent, 
for all the total perpendicular descents from 6 to 15 feet; 
the points of impact are numbered inside the fig. with 
the number of the total fall, for each respectively. The 
top of the shute is only about 15 inches from the wheel, 
in order to set the point of impact as high as possible, 
allowing 3 feet above the upper end of the shute to the 
top of the water in the penstock, which is little enough, 
when the head is to be often run down any considerable 
distance; but where the stream is steady, being always 
nearly the same height in the penstock, 2 feet would be 
sufficient, especially in the greatest total falls. Where 
the quantity is less, raising the shute 1 foot would also 
raise the point of impact nearly the same, and increase 
the power, because 1 foot fall is equal in power to 2 feet 
head, by Art. 61. 

On these principles, to suit the applications of water, 
as represented by fig. 32, I have calculated the follow- 


OF BREAST MILLS. 


175 


Chap, iv.] 

ing table for breast mills. And, in order that the reader 
may fully understand the principles on which it is cal¬ 
culated, let him consider as follows:— 

1. That all the water above the point of impact, called 
head, acts wholly by percussion, and all below said 
point, called fall, acts wholly by gravity, (see Art. GO,) 
these form the 2d and 3d columns. 

2. That half the head, added to the whole fall, con¬ 
stitutes the virtual or effective descent, by Art. Gl, 
which is given in the 4th column. 

3. That if the water were permitted to descend freely 
down the circular sheeting, after it passed the point of 
impact, its velocity would be accelerated by Art. GO, so 
as to be, at the lowest point, equal to the velocity of 
water spouting from under a head equal to the whole 
descent: the maximum velocity of this wheel will conse¬ 
quently be compounded of the velocity to suit the head, 
and the acceleration after it passes the point of impact. 
Therefore, to find the velocity of this wheel, I first mul¬ 
tiply the velocity of the head, in column 5, by .577, (as 
for undershot mills,) which gives the velocity suitable 
to the head; I then, (by the rule for determining the ve¬ 
locity of oversliots,) say as the velocity of water descend¬ 
ing 21 feet, equal to 37.11 feet per second, is to the ve¬ 
locity of the wheel, .10 feet per second, so is the accele¬ 
ration of velocity after it passes the point of impact, to 
the accelerated velocity of the wheel, and these two ve¬ 
locities added, give the velocity of the wheel, which is 
shown in the 6th column. 

4. The velocity of the wheel per second, multiplied by 
GO, and divided by the circumference of the wheel, gives 
the revolutions per minute: see 7th column. 

5. The number of cogs in the cog-wheel multiplied by 
the number of revolutions, per minute, of the water¬ 
wheel, and divided by the rounds in the trundle-head, 
will give the number of revolutions of the stone per 
minute; and, if we divide by the number of revolutions 
the stone is to have, it gives the rounds in the trundle; 
and when fractions arise, take the nearest whole num¬ 
ber: see columns 8, 9 and 10. 


176 


OF BREAST MILLS. 


[CHAP. IV. 

6. The cubochs of power required to turn the stone, 
by Art. 63, divided by the virtual descent, give the cu¬ 
bic feet of water required per second, column 11. 

7. The cubic feet of water divided by the velocity 
allowed to it in the canal, suppose 1.5 feet per second, 
give the area of a section of the canal, column 12. 

8. If the mill is to be double-geared, take the revolu¬ 
tions of the wheel from column 7 of this table, and look 
in column 4 of the undershot table, Art. 70, for the 
number of revolutions nearest to it, and against that 
number you have the gearing that will give a 5 feet 
stone the right motion. 


« 


<?HAP. IV.] 


OF BREAST MILLS 


177 


THE MILL-WRIGHT’S TABLE 

FOR 

BREAST MILLS. 


Calculated lor a water-wheel fifteen feet, and stones five feet in diameter; the 
Avater being shot on in the direction of a tangent, to the circumference of 
the wheel. 


lotal perpendicular descent or fall of the water from the top 
oi the water in the penstock, to ditto in the tail-race. 

Head above the point of impact. 

Fall below the point of impact. 

■ —------ i 

V irtual or effective descent, being half the head added to the 

Jail- 

------—------ 

Velocity of the water per second at the point of impact. 

- ——------ 1 

l 

Velocity of the circumference of the Avheel per second. 

Number of revolutions of a wheel fifteen feet in diameter, per 

minute. 

Cogs in the cog-wheel, for single gear. 

Rounds in the trundle-head. 

Revolutions of the stone, per minute. 

Cubic feet of water required per second. 

Area of a section of the canal, allowing the velocity of the 
water in it to be 1.5 feet per second. 
-——------------ 

feet. 

ft. 

ft. 

feet. 

feet. 

feet. 

No. 

No. 

N. 

No. 

cu.ft. 

sup. ft. 

6 

4.5 

1.5 

3.75 

17.13 

10.61 

13.5 

112 

15 

100.829.8 

19.25 

7 

5. 

2. 

4.5 

18. 

11.3 

14.4 

112 

16 

100.8 

24.83 

16.55 

8 

5.5 

2.5 

5.25 

18.99 

12.07 

15.3 

104 

16 

99.4 

21.29 

14.19 

9 

5.9 

3.1 

6.05 

19.48 

12.53 

16. 

104 

16 

102.7 

18.45 

12.3 

10 

6.2 

3.8 

6.9 

20.16 

13.07 

16.6 

96 

16 

99.6 

16.2 

10.8 

11 

6.5 

4.5 

7.75 

20.64 13.53 

17. 

96 

16 

102. 

14.42 

9.61 

12 

6.8 

5.3 

Q ^ 

o. / 

21.1114.03 

17.81 

96 

17 

100.5 

12.73 

8.49 

13 

6.8 

6.2 

9. 6: 

21.11 14.35 

18.28 

96 

18 

97.5 

11.63 

7.75 

14 

6.9 

7.1 

10.55 

21.3 ] 

14.41 

18.35 

96 

18 

97.8 

10.59 

7.06 

15 

7. 

3. 

11.5 

21.13 14.76 

i 

18.56 

96 

18 

98.4 

9.72 

6.48 

1 

o 

3 I 

4 

5 

6 

7 

8 

91 

10 

11 

12 


12 


























































































178 


OF BREAST MILLS. 


[CHAP. IV- 


Use of the Table for Breast-Mills. 

Having a seat with above 6 feet fall, but not enough 
for an overshot mill, and the water being scarce, so that 
you wish to make the best use of it, should lead you to 
the choice of abreast mill. 

Cast off about 1 foot for fall in the tail-race below the 
bottom of the wheel, if much subject to back water, and 
suppose you have then 9 feet total descent; look for 9 
feet in the first column of the table, and against it you 
have it divided into 5.9 feet head above, and 3.1 feet 
fall below, the point of impact, which is the highest point 
that the water can be fairly struck on the wheel: leaving 
the head 3 feet deep above the shute; which is equal to 
(3.5 feet virtual or effective descent; the velocity of the 
water striking the wheel will be 18.99 feet; and the ve¬ 
locity of the wheel 12.07 feet per second; it will revolve 
16 times in a minute; and, if single-geared, 104 cogs and 
16 rounds, gives the stone 99.4 revolutions in a minute, 
requiring 21.29 cubic feet of water per second; the area 
of a section of the canal must be 14.19 feet, or about 3 
feet deep, and 5 feet wide. If the stones he of any other 
size, it is easy to proportion the gearing to give them 
any required number of revolutions.* 

If you wish to proportion the size of the stones to the 
power of your seat, multiply the cubic feet of water 
your stream affords per second, by the virtual descent in 
column 4, and that product is the power in cubochs; 
then look in the table, in Art. 63, for the size of the 
stone that most nearly suits that power. 

For instance, suppose your stream afford 14 cubic 
feet of water per second, then 14 multiplied by 6.05 
feet virtual descent, produce 84.7 cubochs of power; 
which in the table in Art. 63, comes nearest to 4.5 feet 
for the diameter of the stones: but by the rules laid 
down in Art. 63, the size may be found more exactly. 

* The mill-wright will do well to examine with attention the article in the ap¬ 
pendix, written by the late W.Parkin, a practical and scientific workman, whose 
suggestions are of the utmost importance, as they may lead to the correction of 
errors, which the editor is assured, from his own observations, are almost uni¬ 
versal, the too great velocity, and the too little capacity of water wheels. 


OF OVERSHOT MILLS. 


179 


CHAP. IV.] 

I 

Six cubochs of power are required to every super¬ 
ficial foot of the stones. 


ARTICLE 73. . 

OF OVERSIIOT MILLS. 

Fig. 33, Plate IV., represents an overshot wheel: the 
water is laid on at the top, so that the upper part of the 
column will be in the direction of a tangent with the 
circumference of the wheel, but so that all the water 
may strike within the circle of the wheel. 

The gate is drawn about 30 inches behind the perpen¬ 
dicular line from the centre of the wheel, and the point 
at the sliute ends at said perpendicular with a direction 
a little downwards, which gives the water a little velo¬ 
city downwards to follow the wheel; for if it be directed 
horizontally, the head will give it no velocity downwards, 
and if the head be great, the parabolic curve, which the 
spouting water forms, will extend beyond the outside of 
the circle of the wheel, and it will incline to fly over. 
See Arts. 44 and 60. 

The head above the wheel acts by percussion, as on 
an undershot wheel, and we have shown, Art. 43, that 
the head should be such as to give to the water a velo¬ 
city of 3, for 2 of the wheel. After the water strikes 
the wheel, it acts by gravity; therefore, to calculate the 
power, we must take half the head and add it to the 
fall, for the virtual descent, as in breast mills. 

The velocity of overshot wheels is as the square roots 
of their diameters. See Art. 43. 

On these principles, I have calculated the following 
table for overshot wheels; and, in order that the reader 
may understand it fully, let him consider well the fol¬ 
lowing premises:— 

1. That the velocity of the water spouting on the 
wheel must be one and a half times the velocity of the 
wheel, by Art. 43: then, to find the head that will give 
said velocity, say as the square of 16.2 feet per second, 
is to 4 feet, the head that gives that velocity, so is the 



180 


OF OVERSHOT MILLS. 


[CHAP. IV. 

square of the velocity required, to the head that will 
give the velocity sought for; but to this head, so found, 
we must add a little, by conjecture, to overcome the 
friction of the aperture. See Art. 55. 

In this table, I have added to the heads of wheels of 
from 9 to 12 feet diameter .1 of a foot, and from 12 to 20 
feet I have added one-tenth more, for every foot increase 
of diameter, and from 20 to 30 feet I have added .05 
more to every foot diameters increase; which gives a 30 
feet wheel 1.5 feet additional head, while a 9 feet wheel 
has only one-tenth of a foot, to overcome the friction. 
The reason of this great difference will appear when we 
consider that the friction increases as the aperture de¬ 
creases, and as the velocity increases: still this depends 
much on the form of the gate, for if that be nearly 
square, there will be but little friction; but if very 
oblong, say 24 inches by half an inch, then it will be 
very great. 

The heads thus found, compose the 3d column. 

2. The head, added to the diameter of the wheel, 
makes the total descent, as in column 1. 

3. The velocity of the wheel per second, taken from 
the table in Art. 43, multiplied by 60, and divided by 
the circumference of the wheel, gives the number of 
revolutions of the wheel per minute; as in column 4. 

4. The number of revolutions of the wheel, per mi¬ 
nute, multiplied by the number of cogs in all the driving 
wheels successively, and that product divided by the pro¬ 
duct of all the leading wheels, gives the number of revo¬ 
lutions of the stone per minute, and is found in column 
9, double gear, for 5 feet stones; and in column 12, sin¬ 
gle gear, for 6 feet stones. 

5. The cubochs of power required to drive the stone, 
by table in Art. 63, divided by the virtual or effective 
descent, which is half the head added to the fall, or the 
diameter of the wheel, gives the cubic feet of water re¬ 
quired per second to drive the stone, and is column 13. 

6. The cubic feet required, divided by the velocity 
you intend the water to have in the canal, gives the 
area of a section of the canal. The width multiplied by 
the depth, must always produce this area. See Art. 64. 


CHAP. IV.] OF OVERSHOT MILLS. 181 

7. The number of cogs in the wheel, multiplied by 
the quarters of inches in the pitch, produces the cir¬ 
cumference of the pitch circle; which, multiplied by 7, 
and divided by 22, gives the diameter in quarters of 
inches, which reduced to feet and parts, forms column 
15. The reader may here at once observe how near 
the cog-wheel in the single gear will be to the water; 
that is, how near it is in size to the water-wheel. 


Use of the table. 

Having with care levelled the seat on which you 
mean to build, and found, that after deducting 1 foot for 
fall below the wheel, and a sufficiency for the sinking 
of the head race, according to its length and size, and 
having a total descent remaining sufficient for an over¬ 
shot wheel, suppose 17 feet: then, on looking in the 
first column of the table for the descent nearest to it, 
we find 10.74 feet, and against it a wheel 14 feet diame¬ 
ter: head above the wheel 2.7 feet; revolutions of the 
wheel per minute 11.17; double gears, to give a 5 feet 
stone 98.7 revolutions per minute; single gears to give 
a 6 feet stone 7G.6 revolutions per minute; the cubic 
feet of water required for a 5 feet stone 7.2 feet per se¬ 
cond, and the area of a section of the canal 5 feet: about 
2 feet deep, and 2.5 feet wide. 

If it be determined to proportion the size of the 
stones exactly to suit the power of the seat, it may be 
done as directed in Art. 63. All the rest can be pro¬ 
portioned by the rules by which the table is calculated. 


182 


OF OVERSHOT MILLS 


[CHAP. IV 


THE MILL-WRIGIIT’S TABLE 

FOR 

OVER-SHOT MILLS. 

Calculated for five feet stones , double gear , and six feet stones , 

single gear. 


o 

=■ 5- £L 

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S' 5 


feet. 


10.51 

11.74 
12.94 
14.2 
15.47 

16.74 

17.99 
19.28 
20.5 
21.8 
23.03 
24.34 
25.54 
26.86 

27.99 
29.27 
30.45 
31.57 
32.77 
33.96 
35.15 
36.4 


1 


ft. 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 
21 
22 

23 

24 

25 

26 

27 

28 

29 

30 


CD 

3 S. O 

CD O 

, et. D 5 
3 o g- 

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cr < 

2 o & 

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^ CD CD 

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O o 35 

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3? c £p 

CD r- 

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I— CD CD 


feet. 


1.51 

1.74 
1.94 
2.2 
2.47 

2.74 

2.99 
3.28 
3.5 
3.8 
4.03 
4.34 
4.54 
4.86 

4.99 
5.27 
5.45 
5.57 
5.77 
5.96 
6.15 
6.4 


2 3 


Number of revolutions of the wheel per 
minute. 

Double gear, 5 
feet stones. 

__A_ 

Single gear, 
6 ft. stones. 

Cubic feet of water required per second 
for five feet stones. 

Area of a section of the canal, allowing 
the velocity of the water in it to be 1 
foot per second. 

Diameter of the pitch circle of the great 
cog-wheels for single gear, pitch 43- 
inches. 

No. of cogs urmaster cog-wheel. 

Rounds in the wallower. 

i D°gs in the counter cog-wheel. 

Rounds in the trundle. 

Revolutions of the stone per mi¬ 
nute. 

O 

o 

(Jq 

M 

5' 

Er 

CD 

CD 

O 

0q 

i 

3 

cr 

CD 

i Rounds in the trundle. 

^ Revolutions of the stone per mi¬ 
nute.. 










cu. ft 

sup. ft. 

feet, inches. 

14.3 

54 21 

44 

16 

102.9 

6011 

78. 

11.46 

11.46 

6:9 0-4 12-22 

13. 

54 21 

48 

18 

98. 

60,10 

78. 

10.3 

10.3 


12.6 

6021 

48 

18 

96. 

6611 

75.6 

9.34 

9.34 

7:5 1-4 

12. 

66 23 

48 

17 

97. 

6610 

79.2 

8.53 

8.53 


11.54 

66 21 

48 

17 

99.3 

84 12 

80.7 

7.92 

7.92 

9:5 1-2 

11.17 

72 23 

48 

17 

98.7 

9614 

76.6 

7.2 

7.2 

10:9 3-4 6-22 

10.78 

78 23 

48 

18 

98.3 

9613 

81.9 

6.77 

6.77 


10.4 

78 23 

48 

17 

99.5 

120 16 76. 

6.4 

6.4 

13:6 1-4 2-22 

10.1 

78 21 

48 

18 

96.6 

120 15 

80.8 

6. 

6. 


9.8 

84 

24 

48 

17 

97. 

128 16 

78.4 

5.56 

5.56 

14:5 0-4 8-22 

9.54 

84 

23 

48 

17 

98.3 

128 15 

81.4 

5.32 

5.32 


9.3 

88 

23 

48 

17 

100. 

128 15 

79.3 

5.04 

5.04 


9.1 

88 

23 

48 

17 

98.3 

12815 

77.6 

4.81 

4.81 


8.9 

96 

24 

48 

17 

100.5 

12814 

81.4 

4.57 

4.57 


8.7 

96 

25 

54 

18 

100.2 




4.34 

4.34 


8.5 

96 

25 

54 

17 

103. 




4.19 

4.19 


8.3 

96 

25 

54 

17 

101. 




4. 

4. 


8.19 

96 

25 

54 

17 

99.6 




3.82 

3.82 


8.03 

104 

25 

54 

18 

100.2 




3.7 

3.7 


7.93 

104 

25 

54 

18 

99. 




3.6 

3.6 


7.75 

112 

26 

54 

18 

100.1 




3.4 

3.4 


7.63 

112 

26 

54 18 

98.6 




3.36 

3.36 


4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 


































































183 


Y 


CHAP. IV.] OF OVERSHOT MILLS. 





L/BRAB 


, 



ables. 


1. It appears that single gearing does not well suit 
this construction; because, where the water wheels are 
low, their motion is so slow that the cog-wheels, (if made 
large enough to give sufficient motion to the stone, with¬ 
out having the trundle too small, see Art. 23,) will touch 
the water. And again, when the water wheels are above 
20 feet high, the cog-wheels require to be so high, in 
order to give motion to the stone without having the 
trundle too small, that they become unwieldy; the husk 
also is too high, and the spindle so short as to be incon¬ 
venient. Single gearing, therefore, seems to suit over¬ 
shot wheels only where their diameter is between 12 
and 18 feet, and even then the water-wheel will have 
to run rather too fast, or tlffi trundle be too small, and 
the stones should be at least 6 feet in diameter. 

2. I have, in the preceding tables, supposed the water 
to pass along the canal with 1.5 feet velocity per second; 
but being of opinion that 1 foot per second is nearer the 
proper motion, that is, about 20 yards per minute, the 
cubic feet required per second, will, in this case, be the 
area of a section of the canal, as given in column 14 of 
this table. 

3. Although I have calculated this table for the velo¬ 
cities of the wheels to vary as the square roots of their 
diameters, which makes a 30 feet wheel move 11.99 feet 
per second, and a 12 feet wheel to move 7.57 feet, per 
second, yet they will do to have equal velocity and head, 
which is the common practice among mill-wriglits. But 
for the reasons I have mentioned in Art. 43, I prefer 
giving them the velocity and head assigned in the table, 
in order to obtain steady motion. 

4. Many have been deceived, by observing the ex¬ 
ceedingly slow and steady motion of some very high 
overshot wheels, working forge or furnace bellows, con¬ 
cluding therefrom, that they will work as steadily with 
a very slow, as with any quicker motion, not considering, 
perhaps, that it is the principle of the bellows that re- 




184 OF OYERSnOT MILLS. [CHAP. IV. 

gulates the motion of the wheel, which is different from 
any other resistance, for it soon becomes perfectly equa¬ 
ble, therefore the motion will he uniform, which is not 
the case with mills of any kind. 

5. An opinion is sometimes entertained, that water 
is not well applied by an overshot wheel, because, it is 
said, those buckets which nearly approach a line drawn 
perpendicularly through the centre, either above or be¬ 
low, act on too short a lever. To correct this erroneous 
idea, I have divided the fall of the overshot wheel, fig. 
33, Plate IV., into feet, shown by dotted lines. Now, 
by Art. 53 and 54, every cubic foot of water on the 
wheel produces an equal quantity of power in descend¬ 
ing each perpendicular foot, called a cuboch of power; 
and that because where the lever is shortest, the great¬ 
est quantity of water is contained within the foot per¬ 
pendicular; or, in other words, each cubic foot of water 
is a much longer time, and passes a greater distance, in 
descending a perpendicular foot, than where the lever 
is longest: this exactly compensates for the deficiency 
in the length of lever. See this demonstrated, Art. 54. 
It is true, that the effect of the lower foot is, in prac¬ 
tice, entirely lost, by the running of the water out of 
the buckets. 


Of Mills moved by Reaction. 

We have now treated of the four different kinds of 
mills that are in general use. There is another, the 
invention of, or rather an improvement by, the late in¬ 
genious James Rumsey, which moves by the reaction 
of water.* 

* This is sometimes known by the name of Barker’s mill; several of which 
have been built in different places; but it is believed that they have all been 
abandoned, as they have not in practice answered the expectations which had 
been entertained respecting them. A modification of this mode of applying 
the power of water has, of late years, been extensively used in the United 
States, and been made the subject of several patents. These wheels will be 
noticed in the appendix.— Editor. 


CHAP. V.] RULES AND CALCULATIONS. 


185 


CHAPTER Y. 


ARTICLE 74. 


RULES AND CALCULATIONS. 


The fundamental principle, on which are founded all 
rules for calculating the motion produced by a combina¬ 
tion of wheels, and for calculating the number of cogs to 
be put in them, to produce any motion that is required, 
has been given in Art. 20; and is as follows:— 

If the revolutions that the first moving wheel makes 
in a minute be multiplied by the number of cogs in all 
the driving wheels successively, and the product noted; 
and the revolutions of the last leading wheel be multi¬ 
plied by the number of cogs in all the leading wheels 
successively, and the product noted; these products will 
be equal in all possible cases. Hence, we deduce the 
following simple rules:— 

1st. For finding the motion of the mill-stone; the re¬ 
volutions of the water-wheel, and the cogs in the wheels, 
being given:— 

RULE. 

Multiply the revolutions of the water-wheel per mi¬ 
nute, by the number of cogs in all the driving wheels 
successively, and note the product; and multiply the 
number of cogs or rounds in all the leading wheels suc¬ 
cessively, and note the product; then divide the first 
product by the last, and the quotient is the number of 
revolutions of the stone per minute. 

EXAMPLE. 


Given, the revolutions of the water-wheel per 
minute, - 

No. of cogs in the master cog-wheel 
No. of do. in the counter cog-wheel 
No. of rounds in the wallower 
No. of do. in the trundle 



10.4 
Drivers. 

Leaders. 


186 


RULES AND CALCULATIONS. [CHAP. V. 

Then 10.4, the revolutions of the water-wheel, multi¬ 
plied by 78, the cogs in the master-wheel, and 48, the 
cogs in the counter-wheel, are equal to 38937.6; and 23 
rounds in the wal lower, multiplied by 17 rounds in the 
trundle, are equal to 391, by which we divide 38937.6, 
and it gives 99.5, the revolutions of the stone per minute; 
which are the calculations for a 16 feet wheel, in the 
overshot table. 

2d. For finding the number of cogs to be put in the 
wheels, to produce any number of revolutions required 
to the mill-stone, or to any wheel:— 

RULE. 

Take any suitable number of cogs for all the wheels 
except one; then multiply the revolutions of the first 
mover per minute, by all the drivers, except the one 
wanting, (if it be a driver,) and the revolutions of the 
wheel required, by all the leaders, and divide the great¬ 
est product by the least, and it will give the number 
of cogs required in the omitted wheel, to produce the 
desired revolutions. 

Note. If any of the wheels be for straps, take their 
diameters in inches and parts, and multiply and divide 
with them, as with the cogs. 

EXAMPLE. 

Given, the revolutions of the water-wheel 10.4 

And the cogs in the master-wheel - 78 1 n . 

Ditto in the counter wheel - - - 48 j riveis - 
Rounds in the wallower - - - 23 

The number of the trundle is required, to give the 
stone 99 revolutions. 

Then 10.4, multiplied by 78 and 48, is equal to 
38937.6; and 99, multiplied by 23, is equal to 2277, by 
which divide 38937.6, and it gives 16.66; instead of 
which, I take the nearest whole number, 17, for the 
rounds in the trundle, and find, by rule 1st, that it pro¬ 
duces 99.5 revolutions as required. 

For the exercise of the inexperienced, I have con¬ 
structed fig. 7, Plate XI.; which I call the circle of mo- 


187 


CHAP. V.] RULES AND CALCULATIONS. 

tion, and which serves to prove the fundamental princi¬ 
ple on which the rules are founded ; the first shaft being, 
also, the last of the circle. 


A is 

a cog-wheel of 20 cogs, and is 

a driver. 

B 

do. 

24 

leader. 

C 

do. 

24 

driver. 

D 

do. 

30 

leader. 

E 

do. 

25 

driver. 

F 

do. 

30 

leader. 

G 

do. 

36 

driver. 

H 

do. 

20 

leader. 


But if we trace the circle the backward way, the 
leaders become drivers. 

I is a strap-wheel 14 £ inches diameter, driver. 

K do. 30 do. - leader. 

L cog-wheel 12 cogs. - driver. 

M do. 29 do. - leader. 

MOTION OF THE SHAFTS. 

The upright shaft, and first driver, All 3G revs, in a min. 

BC 30 do. 

DE 24 do. 

FG 20 do. 

IIA 30 do. 

M 4 do., which is 
the shaft of a liopper-boy. 

If this circle be not so formed as to give the first 
and last shafts (which are here the same) exactly the 
same motion, one of the shafts must break as soon as 
they are put in motion. 

The learner may exercise the rules on this circle, un¬ 
til he can form a similar circle of his own; and then*.he 
need never be afraid to undertake to calculate any other 
combination of motion. 

I omit showing the work for finding the motion of the 
several shafts in this circle, and the wheels to produce 
said motion; but leave it for the practice of the learner, 
in the application of the foregoing rules. 


188 


RULES AND CALCULATIONS. [CHAP. V. 


EXAMPLES. 

1st. Given, the first mover API 36 revolutions per 
minute, and first driver A 20 cogs, leader B 24; re¬ 
quired, the revolutions of shaft BC. Answer, 30 revo¬ 
lutions per minute. 

2dly. Given, first mover 36 revolutions per minute, 
drivers 20—24—25, and leaders 24—30—30; required 
the revolutions of the last leader. Answer, 20 revolu¬ 
tions per minute. 

3dly. Given, first mover 20 revolutions per minute, 
and first driver, strap-wheel, 14 4 inches, cog-wheel 12, 
and leader, strap-wheel, 30 inches, cog-wheel 29; re¬ 
quired, the revolutions of the last leader, or last shaft. 
Answer, 4 revolutions. 

4thly. Given, first mover 36 revolutions, driver A 20, 
C 24, leader B 24, D 30; required the number of leader 
F, to produce 20 revolutions per minute. Answer 30 
cogs. 

5thly. Given, first mover 36 revolutions per minute, 
driver A 20, C 24, E 25, driver pulley 144 inches dia¬ 
meter, L 12, and leader B 24, D 30, F 30, M 29; re¬ 
quired the diameter of the strap-wheel K, to give the 
shaft 4, four revolutions per minute. Answer, 30 inches 
diameter. 

The learner may, for exercise, work the above ques¬ 
tions, and every other that he can propose on the circle. 


ARTICLE 75. 

The following are the proportions for finding the cir¬ 
cumference of a circle, its diameter being given, or the 
diameter by the given circumference; namely:— 

As 1 is to 3.1416, so is the diameter to the circumfe¬ 
rence; and as 3.1416 is to 1, so is the circumference to 
the diameter: Or, as 7 is to 22, so is the diameter to the 
circumference; and as 22 is to 7, so is the circumference 
to the diameter. The last proportion makes the diame¬ 
ter a little too large; it, therefore, suits mill-wrights best 





189 


CHAP. V.] RULES AND CALCULATIONS. 

for finding the pitch circle; because the sum of the dis¬ 
tances, from centre to centre, of all the cogs in a wheel, 
makes the circle too short, especially where the number 
of cogs is few, because the distance is taken in straight 
lines, instead of on the circle. In a wheel of 6 cogs only, 
the circle will be so much too short, as to give the dia¬ 
meter 2 2 * parts of the pitch or distance of the cogs too 
short. Hence, we deduce the following 

RULES FOR FINDING THE PITCH CIRCLE. 

Multiply the number of cogs in the wheel by the 
quarters of inches in the pitch, and that product by 7, 
and divide by 22, and the quotient is the diameter in 
quarters of inches, which is to he reduced to feet. 

EXAMPLE. 

Given, 84 cogs 41 inches pitch; required the diame¬ 
ter of the pitch circle. 

Then, by the rule, 84 multiplied by 18, and by 7, is 
equal to 10584; which, divided by 22, is equal to 481— 
quarter inches, equal to 10 feet T inches, for the dia¬ 
meter of the pitch circle required. 


ARTICLE 76. 

A true and expeditious method of finding the diame¬ 
ter of the pitch circle, is to find it in measures of the 
pitch itself that you use. 

RULE. 

Multiply the number of cogs by 7, and divide by 22, 
and you have the diameter of the pitch circle, in measures 
of the pitch, and the 22d parts of said pitch. 

EXAMPLE. 

Given, 78 cogs; required the diameter of the pitch 
circle. Then, by the rule, 



190 


78 

7 


RULES AND CALCULATIONS. 


[CIIAP. V. 


22)546(2444 [ Measures of the pitch for the diameter 
44 j of the circle required. 


106 

88 


18 

Half of which diameter, 12^% of the pitch, is the radius, 
or half diameter, by which the circle is to be swept. 

To use this rule, set a pair of compasses to the pitch, 
and screw them fast, so as not to be altered until the 
wheel is pitched: divide the pitch into 22 equal parts; 
then step 12 steps, on a straight line with the pitch com¬ 
passes, and 9 of these equal parts of the pitch make the 
radius that is to describe the circle. 

To save the trouble of dividing the pitch for every 
wheel, the workman may mark the different pitch which 
he commonly uses, on the edge of his two-foot rule, (or 
make a little rule for the purpose,) and carefully divide 
them there, where they will always be ready for use. 
See Plate IV. fig. 35. 

By these rules, I have calculated the following table 
of the radii of pitch circles of the different wheels com¬ 
monly used, from 6 to 136 cogs. 





CHAP. V.] 


RULES AND CALCULATIONS 


191 


A TABLE 


OF THE 

PITCH CIRCLES OF THE COG-WHEELS 

COMMONLY USED, 

From 6 to 136 cogs, both in measures of the pitch, and in feet, inches and parts. 


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Pitch. 

22 parts. 

1 

22 parts, 
quarters. 

inches. 

3 

0 

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Titch. 

22 parts. 

1 * 

1 

feet. 

22 parts. 

quarters. 

1 

1 

inches. 

| 22 parts. ! 
quarters, 
inches, 
feet. 

6 

1 


2:2: 0 

33 

5 

5 1-2 

1: 

10: 1: 5 1-2 

1:11:2:11 

7 

1 

3.5 

2:3:12 

34 

5 

9 

1: 

10: 3:21 

2: 0:1: 8 

8 

1 

6.7 

3:1: 3 

35 

5 

12 1-2 

1: 

11: 2:14 1-2 

2: 1:0: 5 

1 9 

1 

10.2 

3:2:13 

36 

5 

16 

2: 

0: 1: 8 

2: 1:3: 2j 

10 

1 

13.6 

4:0: 3 

37 

5 

19 1-2 

2: 

1: 0: 1 1-2 2: 2:1:21 l 

11 

1 

17.1 

4:1:17 

38 

6 

1 . 

2: 

1: 2:17 

2: 3:0:10 

12 

1 

20.5 

4:3: 5 

39 

6 

4 1-2 

2: 

2: 1:10 1-2 2: 3:3:15 1 

113 

2 

1.9 

5:0:17 

40 

6 

8 

2: 

3: 0: 4 

2: 4:2:12 

114 

2 

5.3 

5:2: 8 

42 

6 

15 

2: 

4: 1:13 

2: 6:0. 6 

15 

2 

8.8 

5:3:20 

44 

7 


0- 
** • 

5: 3: 0 

2: 7:2: 0 

16 

2 

12.2 

6:1:11 

48 

7 

14 

2: 

8: 1:18 

2:10:1:10 

17 

2 

Id./ 

6:3: 2 

52 

8 

4 

2: 

11: 0:14 

3: 1:0:20 

18 

2 

19.1 

7:0:15 

54 

8 

11 

3: 

0: 2: 1 

3: 2:2:14 

19 

3 

0.6 

7:2: 6 

56 

8 

20 

3: 

1: 3:10 

3: 4:0: 8 

20 

.3 

4.1 

7:3:18 

60 

9 

13 

3: 

4: 2: 6 

3: 6 3:18 

21 

3 

7.5 

8:1: 9 

66 

10 

1 1 

3. 

8: 2:11 

13:11:1: 0 

09 

3 

11. 

8:3: 0 

72 

11 

10 

4: 

0: 2:16 

I 4 : 3:2: 4 

23 

3 

14.5 

9:0:13 

78 

12 

9 

4: 

4: 2:21 

4: 7:3: 8 

2-1 

3 

18. 

9:2: 4 

84 

13 

8 

4: 

8: 3: 4 

5: 0:0:12 

25 

3 

21.5 

9:3:17 , 

88 

14 

0 

4: 

11: 2: 0 

15: 3:0: 0 

26 

4 

3. 

10:1: 8 

90 

14 

7 

5: 

0: 3: 9 

5: 4:1:16 

27 

4 

6.5 

10:2:21 

96 

15 

6 

5: 

4: 3:14 

5: 8:2:20 

j 28 

4 

10. 

11:0:12 

104 

16 

13 

5: 

10: 1: 6 

6: 2:1:18 

29 

4 

13.5 

11:2: 3 

112 

17 

18 

6: 

3: 2:20 

6: 8:0:16 

30 

4 

17. 

11:3:16 

120 

19 

2 

6: 

9: 0:12 

7: 1:3:14 

31 

4 

20.5 

12:1: 7 

128 

20 

8 

7: 

2: 2: 4 

7: 7:2:12 

32 

5 

2. 

12:2:20 

136 

21 

14 

7: 

7: 3:18 

8: 1:1:10 

|l 

2 

3 

4 

5 

6 

7 





























































192 


RULES AND CALCULATIONS. [CHAP. V. 


Use of the foregoing Table. 

Suppose you are making a cog-wheel with 66 cogs, 
look for the number in the 1st or 4th column, and against 
it, in the 2d or 5th column, you find 10.11; that is, 10 
steps of the pitch (you use) in a straight line, and 11 of 
22 equal parts of said pitch added, make the radius that 
is to describe the pitch circle. 

The 3d, 6th and 7tli columns contain the radius in 
feet, inches, quarters and 22 parts of a quarter, which 
may be made use of in roughing out timber, and fixing 
the centres that the wheels are to run in, so that they 
may gear to the right depth; but on account of the dif¬ 
ference in the parts of the same scales or rules, and the 
difficulty of setting the compasses exactly, they can 
never be true enough for the pitch circles. 

RULE COMMONLY PRACTISED. 

Divide the pitch into 11 equal parts, and take in your 
compasses 7 of those parts, and step, on a straight line, 
counting four cogs for every step, until you come up to 
the number in your wheel; if there be an odd one at 
last, take 1 of a step—if two be left, take 1 of a step— 
if 3 be left, take t of a step, for them; and these steps 
added, make the radius or sweep-staff of the pitch cir¬ 
cle; but on account of the difficulty of making these 
divisions sufficiently exact, there is little truth in this 
rule; and where the number of cogs is few, it will make 
the diameter too short, for the reasons formerly men¬ 
tioned. 

The following geometrical rule is more true, and, in 
some instances, more convenient. 

RULE. 

Draw the line AB, plate IV., fig. 34, and draw the line 
0.22 at random, then take the pitch in your compasses, 
and beginning at the point 22, step 11 steps towards A, 
and 3-J- steps to point X, towards 0, draw the line AG 
through the point X; draw the line DC parallel to AB, 


193 


CnAP. V.] RULES AND CALCULATIONS. 

and, without having altered your compasses, begin at 
point 0, and step both ways, as you did on AB; then, 
from the respective points, draw the cross lines parallel 
to 0.22; and the distance from the point, where they 
cross the line AC, to the line AB, will be the radius of 
the pitch circles for the number of cogs respectively, as 
in the figure. If the number of cogs be odd, say 21, the 
radius will be between 20 and 22. 

This will also give the diameter too short, if the 
wheels have but few cogs; but where the number of 
cogs is above 20, the error is imperceptible. 

All these rules are founded on the proportion, that, 
as 22 is to 7, so is the circumference to the diameter. 


ARTICLE 77. 

CONTENTS OF GARNERS, HOPPERS, ETC., IN BUSHELS. 

A Table of English Dry Measure . 

The bushel contains 
2150«4 solid inches. 
Therefore, to mea¬ 
sure the contents of 
any garner, take the 
following 

RULE. 

Multiply its length in inches by its breadth in inches, 
and that product by its height in inches, and divide the 
last product by 2150.4, and it will give the bushels it 
contains. 

But, to shorten the work decimally; because 2150.4 
solid inches make 1.244 solid feet, multiply the length, 
breadth and height, in feet, and decimal parts of a foot, 
by each other, and divide by 1.244, and it will give the 
contents in bushels. 

EXAMPLE. 

Given, a garner 6.25 feet long, 3.5 feet wide, 10.5 feet 
high; required, its contents in bushels. Then, 6.25 mul- 
13 




















194 


RULES AND CALCULATIONS. [CIIAP. V. 

tiplied by 3.5 and 10.5, is equal to 229.087; which, di¬ 
vided by 1.244, gives 184 bushels and 6 tenths. 

To find the contents of a hopper, take the following 

RULE. 

Multiply the length by the width at the top, and that 
product by one-third of the depth, measuring to the very 
point, and divide by the contents of a bushel, either in 
inches or decimals, and the quotient will be the contents 
in bushels. 

EXAMPLE. 

Given, a hopper 42 inches square at the top, and 24 
inches deep; required, the contents in bushels. 

Then 42 multiplied by 42, and that product by 8, is 
equal to 14112 solid inches; which, divided by 2150.4, 
the solid inches in a bushel, gives 6.56 bushels, or a lit¬ 
tle more than 61 bushels. 

To make a garner to hold any given quantity, having 
two of its sides given, pursue the following 

RULE. 

Multiply the contents of 1 bushel by the number of 
bushels the garner is to hold; then multiply the given 
sides into each other, and divide the first by the last 
product, and the quotient will be the side wanted, in 
the same measure by which you have wrought in. 

EXAMPLE. 

Given, two sides of a garner 6.25 by 10.5 feet, re¬ 
quired the other side, to hold 184.6 bushels. 

Then, 1.244, multiplied by 184.6, is equal to 229.642, 
which, divided by the product of the two sides, 65.625, 
the quotient is 3.5 feet for the side wanted. 

To make a hopper to hold any given quantity, having 
the depth given. 

RULE. 

Divide the inches contained in the bushels it is to hold 
by l-3d the depth in inches, and the quotient will be the 
square of one of the sides at the top in inches. 


CHAP. VI.] OF SPUR GEARS. 195 

Given, the depth 24 inches, required the sides to hold 
6.56 bushels. 

Then 6.56 multiplied by 2150.4, equal to 14107.624; 
which, divided by 8, gives 1764, the square root of which 
is 42 inches; which is the length of the sides of the hop¬ 
per wanted. 


CHAPTER VI. 

ARTICLE 78. 

OF THE DIFFERENT KINDS OF GEARS AND FORMS OF COGS. 

Ix order to conceive a just idea of the most suitable 
form or shape of cogs in cog-wheels, we must consider 
that they describe, with respect to the pitch circles, a 
figure called an Epicycloid. 

And when one wheel works in cogs set in a straight 
line, such as the carriage of a saw-mill, the cogs or 
rounds, moving out and in, form a curve called a Cy¬ 
cloid. 

To describe this figure, let us suppose the large circle 
in Plate V., fig. 37, to move on the straight line from 0 
to A; then the point 0, in its periphery, will describe 
the arch 01) A, wdiich is called a Cycloid; and by the 
way in which the curve joins the line, we may conceive 
what should be the form of the point of the cog. 

Again, suppose the small circle to run round the 
large one, then the point o, in the small circle, w T ill de¬ 
scribe the arch 0 b C, called an Epicycloid; by which 
we may conceive what should be the form of the point 
of the cogs. But in common practice we generally let 
the cogs extend but a short distance past the pitch cir¬ 
cle, so that their precise form is not so important. 


ARTICLE 79. 

OF SPUR GEARS. 

The principle of spur gears is that of two cylinders 
rolling on each other, with their shafts or axes truly pa- 




196 


OF SPUR GEARS. 


[CHAP. VI. 

rallel. Here the touching parts move with equal velo¬ 
city, and have, therefore, but little friction; but to pre¬ 
vent these cylinders from slipping, we are obliged to in¬ 
dent or to set cogs in them. 

It appears to me that, in this kind of gear, the pitch 
of the driving wheel should be a little larger than that 
of the leading wheel, for the following reasons:— 

1. If there is to be any slipping, it will be much easier 
for the driver to slip a little past the leader, than for 
the cogs to have to force the leader a little before the 
driver, which would be very hard on them. 

2. If the cogs should bend any by the stress of the 
work, as they assuredly do, this will cause those that 
are coming into gear to touch too soon, and rub hard at 
entering. 

3. It is much better for cogs to rub hard as they are 
going out of gear, than as they are coming in; because 
then they work with the grain of the wood, whereas, 
at entering, they work against it, and would wear much 
faster. 

The advantage of this kind of gear is, that we can 
make the cogs as wide as we please, so that their bear¬ 
ing may be so large that they will not cut, but only 
polish each other, and wear smooth; therefore, they will 
last a long time. 

Their disadvantages are, 

1st. That if the wheels be of different sizes, and the 
pitch circles are not made to meet exactly, they will not 
run smoothly. And, 

2dly. AVe cannot, conveniently, change the direction 
of the shafts. 

Fig. 38, Plate V., shows two spur-wheels working into 
each other; the dotted lines show the pitch circles, 
which must always meet exactly. The ends of the 
cogs are made circular, as is commonly done; but if 
they were made true epicycloids, adapted to the size of 
the wheels, they would work with less friction, and, con¬ 
sequently, be much better. 


OF FACE GEARS. 


197 


CHAP. VI.] 

. -Fig. 39 is a spur and face wheel, or wallower, whose 
pitch circles should always meet exactly. 

The rule for describing the sides of the cogs, so as 
nearly to approach the figure of an epicycloid, is as fol¬ 
lows ; namely: Describe a circle a little inside of the pitch 
circle, for the point of your compasses to he set in, so as 
to describe the sides of the cogs, (as the four cogs at A, 
Plate V. fig. 38—39,) as near as you can to the curve of 
the epicycloid that is formed by the little wheel moving 
round the great one; the greater the difference between 
the great and small wheels, the greater distance must 
this circle be within the pitch circle: in doing this pro¬ 
perly, much will depend upon the judgment of the work¬ 
man.* 




ARTICLE 80. 

OF FACE GEARS. 

The principle of face gears is that of two cylinders 
rolling with the side of one on the end of the other, 
their axes being at right angles. Here, the greater the 


* The following is Mr. Charles Taylor’s rule for ascertaining the true cy- 
cloidical or epicycloidical form for the point of cogs :— 

Make a segment of the pitch circle of each wheel, which gear into each other; 
fasten one to a plain surface, and roll the other round it, as shown Plate V. fig. 
37, and, with a point in the moveable segment, describe the epicycloid o b c; set 
off at the end o one-fourth part of the pitch for the length of the cog outside of 
the pitch circle. Then fix the compasses at such an opening, that with one leg 
thereof in a certain point, (to be found by repeated trials,) the other leg will 
trace the epicycloid from the pitch circle to the end of the cog: preserve the 
set of the compasses, and through the point where the fixed leg stood, sweep a 
circle from the centre of the wheel, in which set one point of the compasses to 
describe the point of all the cogs of that wheel whose segment was made fast to 
the plane. 

If the wheels be bevel gear, this rule may be used to find the true form of 
both the outer and inner ends of the cogs, especially if the cogs be long, as the 
epicycloid is different in different circles. In making cast iron wheels, it is 
absolutely necessary to attend to forming the cogs to the true epicycloidal figure, 
without which they will grind and wear rapidly. 

The same rule serves for ascertaining the cycloidical form of a right line of 
cogs, such as those of a saw-mill carriage, &c., or of cogs set inside of a circle 
or hollow cone. Where a wheel works within a wheel, the cogs require a very 
different shape. 



198 OF PACE GEARS. [CHAP. VI. 

bearing, and the less the diameter of the wheels, the 
greater will be the friction; because the touching parts 
move with different velocities—therefore the friction 
will be great. 

The advantages of this kind of gear are, 

1st. Their cogs stand parallel to each other; there¬ 
fore, moving them a little out of or in gear, does not 
alter the pitch of the bearing parts of the cogs, and they 
will run smoother than spur gears, when their centres 
are out of place. 

2dly. They serve for changing the direction of the 
shafts. 

Their disadvantages are, 

1st. The smallness of the bearing, so that they wear 
out very fast.* 

2dly. Their great friction and rubbing of parts. 

The cogs for small wheels are generally round, and. 
put in with round shanks. Great care should be taken 
in boring the holes for the cogs with a machine, to di¬ 
rect the auger straight, that the distance of the cogs may 
be equal, without dressing. And all the holes of all the 
small wheels in a mill should be bored with one auger, 
and made of one pitch; then the miller may keep by him 
a quantity of cogs ready turned to a gauge, to suit the 
auger; and when any fail, he can put in new ones, with¬ 
out much loss of time. 

Fig. 40, Plate Y. represents a face cog-wheel working 
into a trundle; showing the necessity of having the cor¬ 
ners of the sides of the cogs sniped, or worked off in a 
cycloidal form, to give liberty for the rounds to enter be¬ 
tween the cogs, and pass out again freely. To describe 
the sides of the cogs of the right shape to meet the rounds 
when they get fairly into gear, as at c, there must be a 
circle described on the ends of the cogs, a little outside 
of the pitch circle, for the point of the compasses to be 
set in, to describe the ends of the cogs; for if the 

point be set in the pitch circle, it will leave the inner 

, » 

* If the bearing of the cogs be small, and the stress so great that they cut one 
another, they will wear exceedingly fast; but if it be so large, and the stress so 
light, that they only polish one another, they will last very long. 


CHAP. VI.] OF BEVEL GEARS. 199 

% 

corners too full, and make the outer ones too scant. 
The middle of the cog is to be left straight, or nearly 
so, from bottom to top, and the side nearly flat, at the 
distance of half the diameter of the round, from the end, 
the corners only being worked off to make the ends of 
the shape in the figure; because, when the cog comes 
fully into gear, as at c, the chief stress is there, and there 
the bearing should be as large as possible. The smaller 
the cog-wheel, the larger the trundle; and the wider the 
cogs, the more will the corners require to be worked off. 
Suppose the cog-wheel to turn from 40 to b, the cog 40, 
as it enters, will bear on the lower corner, unless it be 
sufficiently worked off; when it comes to c, it will be 
fully in gear: and if the pitch of the cog-wheel be a little 
larger than that of the trundle, the cog a, will bear as it 
goes out, and let c fairly enter before it begins to bear. 

Suppose the plumb line A B to hang directly to the 
centre of the cog-wheel, the spindle is, by many mill¬ 
wrights, set a little before the line or centre, that the 
working round, or stave, of the trundle may be fair with 
said line, and meet the cog fairly as it comes to bear; by 
this means, also, the cogs enter with less, and go out with 
more friction. Whether there be any real advantage in 
thus setting the spindle foot before the centre plumb line, 
does not seem to be determined. 


ARTICLE 81. 

OF BEVEL GEARS. 

The principle of bevel gears is that of two cones roll¬ 
ing on the surface of each other, their vertexes meeting 
in a point, as at A, fig.‘41, Plate Y. Here the touching 
surfaces move with equal velocities in every part of the 
cones; therefore, there is but little friction. These cones, 
when indented, or fluted, with teeth diverging from the 
vertex to the base, to prevent them from slipping, be¬ 
come bevel gear; and as these teeth are very small- at the 



200 


OF BEVEL GEARS. 


[CHAP. VI. 

point or vertex of tlie cone, they may be cut off 2 or 3 
inches from the base, as 19 and 25, at B; they then have 
the appearance of wheels. 

To make these wheels a suitable size for any number 
of cogs you choose to have to work into one another, 
take the following 


RULE. 

Draw lines to represent your shafts, in their proper 
direction, with respect to each other, to intersect A; then 
take from any scale of equal parts, as feet, inches, or 
quarters, as many parts as your wheels are to have cogs, 
and at that distance from the respective shafts, draw the 
dotted lines a, b, c, d, for 21 and 20 cogs; and from where 
they cross at e, draw e, A. On this line, which makes 
the right bevel, the pitch circles of the wheels will meet, 
to contain that proportion of cogs of any pitch. 

Then, to determine the size of the wheels to suit any 
particular pitch, take from the table of pitch circles the 
radius in measures of the pitch, and apply it to the centre 
of the shaft, and the bevel line A e, taking the distance 
at right angles with the shaft; and it will show the point 
in which the pitch circles will meet, to suit that particu¬ 
lar pitch. 

By the same rule, the sizes of the wheels at B and C 
are found. 

Wheels of this kind, when made of cast iron, answer 
exceedingly well. 

The advantages of this kind of gear are, 

1. They have very little friction, or sliding of parts. 

2. We can make the cogs of any width of bearing we 
choose; therefore they will wear a great while. 

3. By them we can set the shafts in any direction de¬ 
sired, to produce the necessary movements. 

Their disadvantage is, 

They require to be kept exactly of the right depth in 
gear, so that the pitch circles meet constantly, else they 
will not run smooth, as is the case with spur gears. 

The universal joint, as represented fig. 43, may be 


201 


CHAP. VI.] MATCHING WHEELS, ETC. 

applied to communicate motion, instead of bevel gear, 
where the motion is to be the same, and the angle not 
more than 30 or 40 degrees. This joint may be con¬ 
structed by a cross, as in the figure, or by four pins, 
fastened at right angles on the circumference of a hoop 
or solid ball. It may sometimes serve to communicate 
the motion, instead of two or three face wheels. The 
pivots, at the end of the cross, play in the ends of the 
semicircles. It is best to screw the semicircles to the 
blades, that they may be taken apart. 


ARTICLE 82. 

OF MATCHING WHEELS TO MAKE THE COGS WEAR EVEN. 

Great care should be taken, in matching or coupling 
the wheels of a mill, that their number of cogs be not 
such that the same cogs will often meet; because, if two 
soft ones meet often, they will both wear away faster 
than the rest, and destroy the regularity of the pitch, 
whereas, if they are continually changing, they will wear 
regular, even if they be at first a little irregular. 

For finding how often wheels will revolve before the 
same cogs meet again, take the following 


RULE. 

1. Divide the cogs in the greater wheel by the cogs 
in the lesser; and if there be no remainder, the same 
cogs will meet once every revolution of the great wheel. 

2. If there be a remainder, divide the cogs in the 
lesser wheel by the said remainder, and if it divide them 
equally, the quotient shows how often the great wheel 
will revolve before the same cogs meet. 

3. But if it will not divide equally, then the great 
wheel will revolve as often as there are cogs in the small 
wheel, and the small wheel as often as there are cogs 
in the large wheel, before the same cogs meet: they 
never can be made to change more frequently than this. 



202 


ROLLING SCREENS AND FANS. [CHAP. VI. 


EXAMPLE. 

* 

Given, wheels of 13 and 17’cogs; required, how often 
each will revolve before the same cogs meet again. 

Then 13)17(1 
13 

4)13(3 

12 Answer. 

— Great Avlieel 13, and 

1 Small wheel 17 revolutions. 


AllTICLE 83. 

THEORY OF ROLLING SCREENS AND FANS, FOR SCREENING AND FAN¬ 
NING THE WHEAT IN MILLS. 

Let fig. 42, Plate V. represent a rolling screen and 
fan, fixed for cleaning wheat in a merchant mill. DA 
the screen, AF the fan, AB the wind tube, 3 feet deep 
from a to b, and 4 inches wide, in order that the grain 
may have a good distance to fall through the wind, to 
give time and opportunity for the light parts to he car¬ 
ried forward, away from the heavy parts. Suppose the 
tube to he of equal depth and width for the whole of 
its length, except where it communicates with the tight 
boxes or garners under it; namely: C for the clean wheat, 
S for the screenings and light wheat, and c for the cheat, 
chaff, &c. Now it is evident that if wind be driven into 
the tube at A, and if it can no where escape, it will pass 
on to B, with the same force as at A, let the tube be of 
any length or direction; and any thing which it will 
move at A, it will carry out at B, if the tube he of an 
equal size all the way. 

It is also evident that if we shut the holes of the fan 
at A and F, and let no wind into it, none can be forced 
into the tube; hence, the best way to regulate the blast 



CHAP. VI.] ROLLING SCREENS AND FANS. 203 

is, to fix shutters sliding at the air-holes, to give more 
or less feed, or air, to the fan, so as to produce a blast 
sufficient to clean the grain. 

The grain enters, in a small stream, into the screen 
at D, where it passes into the inner cylinder. The 
screen consists of two cylinders of sieve wire; the in¬ 
most one lias the meshes so open as to pass all the wheat 
through*it to the outer one, retaining only the white 
caps, large garlic, and every thing larger than the grain 
of the wheat, which falls out at the tail A. 

The outer cylinder is so close in the meshes, as to re¬ 
tain all good wheat, but to sift out the cheat, cockle, 
small wheat, garlic, and every thing less than good 
grains of wheat; the wheat is delivered out at the tail 
of the outer cylinder, which is not quite as long as the 
inner one, whence it drops into the wind tube at a; and 
as it falls from a to b, the wind carries off every thing 
lighter than good wheat; namely: cheat, chaff, light 
garlic, dust, and light rotten grains of wheat; but in 
order to effect this completely, it should fall at least 3 
feet through the current of wind. 

The clean wheat falls into the funnel b, and thence 
into the garner C, over the stones. The light wheat, 
screenings, &c. fall into garner S, and the chaff settles 
into the chaff room c. The current slackens in passing 
over this room, and drops the chaff, but resumes its full 
force as soon as it is over, and carries out the dust through 
the wall at B. To prevent the current from slackening 
too much, as it passes over S and c, and under the 
screen, make the passages, where the grain comes in 
and goes out, as small as possible, not more than half 
an inch wide, and as long as necessary. If the wind 
escapes any where but at B, it defeats the object, and 
carries the dust into the mill. Yalves may be fixed to 
shut the passages by a weight or spring, so that the 
weight of the wheat, falling on them, will open them 
just enough to let it pass without suffering any wind to 
escape. 

The fan is to be so set as to blow both the wheat and 
screenings, and carry out the dust. It is to be recol- 


204 


OF GUDGEONS. 


[cnAP. YII. 

lected, also, that the wind cannot escape into the garners 
or screen-room, if they are tight; for as soon as they are 
full no more can enter. 

By careful attention to the foregoing principle, we 
may fix fans to answer our purposes. 

The principal things to be observed in fixing screens 
and fans are: 

1. Give the screen 1 inch to the foot fall, and between 
15 and 18 revolutions in a minute. 

2. Make the fan blow strong enough, let the wings 
be 3 feet wide, 20 inches long, and revolve 140 times 
in a minute. 

3. Regulate the blast by giving more or less feed of 
wind. 

4. Leave no place for the wind to escape but at the 
end through the wall. 

5. Wherever you want it to blow hardest, there make 
the tube narrowest. 

6. Where you want the chaff and cheat to fall, there 
widen the tube sufficiently. 

7. Make the fans blow both the wheat and screenings, 
and carry the dust clear out of the mill. 

8. The wind tube may be of any length, and either 
crooked or straight, as may best suit; but no where 
smaller than where the wheat falls. 


CHAPTER VII. 


ARTICLE 84. 

OF GUDGEONS, THE CAUSE OF TIIEIR HEATING AND GETTING LOOSE, 

AND REMEDIES THEREFOR. 

b The cause of gudgeons heating is the excessive fric¬ 
tion of their rubbing parts, which generates the heat in 
proportion to the weight that presses the rubbing sur¬ 
faces together, and the velocity with which they move. 



OF GUDGEONS. 


205 


CHAP. VII.] 

The cause of their getting loose is, their heating, and 
burning the wood, or drying it, so that it shrinks in the 
bands, and gives the gudgeons room to work. 

To avoid these effects, 

1. Increase the surface of contact, or rubbing parts, 
and, if possible, decrease their velocity; so much heat 
will not then be generated. 

2. Conduct the heat away from the gudgeon as fast as 
it is generated. 

To increase the surface of contact, without increasing 
the velocity, lengthen the neck or bearing part of the 
gudgeon. If the length be doubled, the weight will be 
sustained by a double surface, and the velocity remain 
the same; there will not then be so much heat gene¬ 
rated ; and, even supposing the same quantity of heat 
generated, there will be a double surface exposed to air, 
to convey it away, and a double quantity of matter, in 
which it will be diffused. 

To convey the heat away as fast as generated, cause 
a small quantity of water to drop slowly on the gudgeon. 
A small is better than a large quantity; it should be 
just sufficient to keep up the evaporation, and not destroy 
the polish made by the grease, which it will do, if the 
quantity be too great; and this will let the box and gud¬ 
geon come into contact, which will cause both to wear 
rapidly away. 

The large gudgeons, for heavy wheels, are usually 
made of cast iron. Fig. 6, Plate XI., is a perspective 
view of one of the best form; a a a a are four wings, at 
right angles with each other, extending from side to side 
of the shaft. These wings are larger, every way, at the 
end that is farthest in the shaft, than at the outer end, 
for convenience in casting them, and also, that the bands 
may drive on tight, one over each end of the wings. 
Fig. 4 is an end view of the shaft, with the gudgeon in 
it and a band on the end; these bands, being put on hot, 
become very tight as they cool, and, if the shaft be dry, 
will not get loose, but will do so if green; but, by driving 
a few wedges along side of each wing, it can be easily 
fastened, by any ordinary hand, without danger of 
moving it from the centre. 


206 


OF GUDGEONS. 


[CHAP. VII. 

One great use of these wings is, to convey away the 
heat from the gudgeon to the bands, which are in con¬ 
tact with the air; by thus distributing it through so much 
metal, with so large a surface exposed to the air, the heat 
is carried off as fast as generated, and therefore can 
never accumulate to a degree sufficient to burn loose, as 
it is apt to do in common gudgeons of wrought iron. 

These gudgeons should be made of the best hard me¬ 
tal, well refined, in order that they may wear well, and 
not be subject to break; but of this there is but little 
danger, if the metal be good. I propose, sometimes, to 
have wings cast separate from the neck, as represented 
in fig. 4, Plate XI.; where the inside light square shows 
a mortise for the steeled gudgeon, fig. 8, to be fitted into, 
with an iron key behind the wings, to draw the gudgeon 
tight, if ever it should work loose: when thus made, it 
may be taken out, at any time, to repair. 

This plan would do well for step-gudgeons for heavy 
upright shafts, such as those of tub-mills. 

When the neck is cast with the wings, the square part 
in the shaft need not be larger than the light square re¬ 
presenting the mortise.* 


* Grease of any kind, used with a drill, in boring cast iron, prevents it from 
cutting, but will, on the contrary, make it cut wrought iron, or steel much faster. 
This quality in cast iron renders it most suitable for gudgeons, and may be the 
principal cause why cast iron gudgeons have proved much better than any one 
expected. Several of the most experienced and skilful mill-wrights and millers 
assert that they have found cast gudgeons to run on cast boxes better than on 
stone or brass. In one instance they have carried heavy overshot wheels, which 
turned seven feet mill-stones, they have run for ten years, doing much work, 
and have hardly worn off the sand marks. 


CHAP. VIII.] 


OF MILL-DAMS. 


207 


CHAPTER VIII. 

ARTICLE 85. 

ON BUILDING MILL-DAMS, LAYING FOUNDATIONS, AND BUILDING 

MILL-WALLS. 

There are several points to be attained, and dangers 
to be guarded against, in building mill-dams. 

1. Construct them so, that the water, in tumbling 
over them, cannot undermine their foundations at the 
lower side.* 

2. And so that heavy logs, or large pieces of ice. 
floating down, cannot catch against any part of them, 
but will slide easily over.')* 


* If you have not a foundation of solid rocks, or of stone, so heavy that the 
water will never move them, there should be such a foundation made with great 
stones, not lighter than mill-stones, (if the stream be heavy and the fall great,) 
well laid, as low, and as close as possible, with their up-stream end lowest, to 
prevent any thing from catching under them. But if the bottom be sand or clay, 
make a foundation of the trunks of long trees, laid close together on the bottom 
of the creek, with their butt ends down-stream, as low and as close as possible, 
across the whole tumbling space. On these the dam may be built, either of 
stone or wood, leaving 12 or 15 feet below the breast or fall, for the water to 
fall upon. See fig. 3, Plate X., which is a front view of a log dam, showing the 
position of the logs; also, of the stones in the abutments. 

f If the dam be built of timber, small stones, &c., make the breast perpen¬ 
dicular, with straight logs, laid close one upon one another, putting the largest, 
longest, and best logs on the top; make another wall of logs 12 or 15 feet up¬ 
stream, laying them close together, to prevent lamprey eels from working 
through them; they are not to be so high as the other, by 3 feet; tie these 
walls together, at every 6 feet, with cross logs, with the butts down-stream, 
dove-tailed and bolted strongly to the logs of the lower wall, especially the 
upper log, which should be strongly bolted down to them. The spaces between 
these log walls are to be filled up with stones, gravel, &c. Choose a dry season 
for this work; then the water will run through the lower part while you build 
the upper part tight. 

To prevent any thing from catching against the top log, flag the top of the 
dam with broad or long stones, laying the down-stream end on the up-stream 
side of the log, to extend a little above it, the other end lowest, so that the next 
tier of stones will lap a little over the first; still getting lower, as you advance 
up-stream. This will glance logs, &c. over the dam, without their catching 
against anything. If suitable stones cannot be had, I would recommend strong 
pfank or small logs, laid close together, with both ends pinned to the top logs 
of the wall, the up-stream end being 3 feet lower than the other. But if plank 
is to be used, there need only be a strong frame raised on the foundation logs, 
to support the plank or the timber it is pinned to. See a side view of this frame, 
fig. 45, Plate IV. Some plank the breast to the front posts, and fill the hollow 


208 


OF BUILDING MILL-DAMS. 


[CHAP. VIII. 

3. Build them so that the pressure or force of the 
current of the water will press their parts more firmly 
together.* 

4. Give them a sufficient tumbling space to vent all 
the water in time of freshets.-)* 

5. Make the abutments so high that the water will 
not overflow them in time of freshets. 

G. Let the dam and mill be a sufficient distance apart, 
so that the dam will not raise the water on the mill, in 
time of high floods. J 

space with stones and gravel; but this may be omitted, if the foundation logs 
are sufficiently long up-stream, under the dam, to prevent the "whole from floating 
away. First, stone, and then gravel, sand, and clay, are to be filled in above 
this frame, so as to stop the water. If the abutments be well secured, the dam 
will stand well. 

A plank laid in a current of water, with the up-stream end lowest, set at an 
angle of 22^ degrees, with the horizon or current of the water, will be held 
firmly to its place by the force of the current, and, in this position, it requires 
the greatest force to remove it; and the stronger the current, the firmer it is 
held to its place;—this points out the best position for the breast of dams. 

* If the dam be built of stone, make it in the form of an arch or semicircle, 
standing up-stream, and endeavour to fix strong abutments on each side, to sup¬ 
port the arch; then, in laying the stones, put the widest end up-stream, and the 
more they are forced down-stream, the tighter they will press together. All 
the stones of a dam should be laid with their up-stream ends lowest, and the 
other end lapped over the preceding, like the shingles or tiles of a house, to 
glance every thing smoothly over, as at the side 3, of fig. 3, Plate X. The 
breast may be built up with stone, either on a good rock or log foundation, put¬ 
ting the best in front, leaning a little up-stream, and on the top lay one good 
log, and another 15 feet up-stream on the bottom, to tie the top log to, by several 
logs, with good butts, down-stream, dove-tailed and bolted strongly, both at 
bottom and top of the top and up-stream logs; fill in between them with stone 
and gravel, laying large stones slanting next the top log, to glance any thing 
over it. This will be much better than to build all of stone; because if one at 
top gives way, the breach will increase rapidly, and the whole go down to the 
bottom. 

f If the tumbling space be not long enough, the water will be apt to overflow 
the abutments; and if they be of earth or loose stones, they will be broken down, 
and perhaps, a very great breach made. If the dam be of logs, the abutments 
will be best made of stone, laid as at the side 3, in fig. 3; but if stone is not to 
be had, they must be made of wood, although it will be subject to rot soon, being 
above water. 

J I have, in many instances, seen a mill set so close to the dam, that the 
pierhead, or forebay, was in the breast, so that, in case of a leak or breach 
about the forebay, or mill, there is no chance of shutting off the water, or con¬ 
veying it another way; but all must be left to its fate. Such mills are frequently 
broken down, and carried away; even the mill-stones are sometimes carried a 
considerable distance down the stream, buried under the sand, and never found. 

The great danger from this error will appear more plainly, if we suppose six 
mills on one stream, one above the other, each at the breast of the dam, and a 
great flood to break the first or uppermost dam, say through the pierhead, carrying 
with it the mill, stones and all: this so increases the flood, that it overflows the 
next dam, which throws the water against the mill, and it is taken away; the 
water of these two dams has now so augmented the flood, that it carries every 
mill before it until it comes to the dam of the sixth, which it sweeps away also : 
but suppose this dam to be a quarter of a mile above the mill, which is set well 


CHAP. VIII.] 


ON BUILDING MILL-WALLS. 


209 


ARTICLE 80. 


ON BUILDING MILL-WALLS. 


The principal things to be considered in building mill- 
walls, are, 

1. To lay the foundations with large, good stones, so 
deep as to be out of danger of being undermined, in case 
of such an accident as the water breaking through at 
the mill.* 

2. Set the centre of gravity, or weight of the wall, on 
the centre of its foundation.*}' 


into the bank, the extra water that is thrown into the canal, runs over at the 
waste left in its banks for the purpose; and the water having a free passage by 
the mill, does not injure it, whereas, had it been at the breast of the dam, it 
must have gone away with the rest. A case, similar to this, actually happened 
in Virginia, in 1794; all the mills and dams on Falling Creek, in Chesterfield 
county, were carried away at once, except the lowest, (Mr. Wardrope’s) whose 
dam, having broke, the year before, was rebuilt a quarter of a mile higher up ; 
by which means this mill w r as saved. 

* If the foundation be not good, but abounding w r ith quick-sands, the wall 
cannot be expected to stand, unless it be made good by driving piles until they 
meet the solid ground; on the top of these may be laid large, flat pieces of timber, 
for the w r alls to be built on; they will not rot under w’ater, w’hen constantly 
excluded from the air. 

f It is a common practice to build w T alls plumb outside, and to batter them 
from the inside; which throw's their centre of gravity to one side of their base. 
If, therefore, it settles any, it will incline to fall outw'ards. Mill-walls should be 
battered so much outside, as to be equal to the offset inside, to cause the W'hole 
weight to stand on the centre of the foundation, unless it stands against a bank, 
as the wall next the w r agon, in Plate VIII. The bank is very apt to press the 
w’all inw’ards, unless it stands battering. In this case, build the side against the 
bank plumb, even w'ith the ground, and then begin to batter it inw’ards. The 
plumb rules should be made a little widest at the upper end, so as to give the 
wall the right inclination, according to its height; to do which take a line, the 
length equal to the height of the wall, set one end, by a compass point, in the 
lower end of the plumb rule, and strike the plumb line; then move the other 
end just as much as the w'all is to be battered in the whole height, and it will 
show the inclination of the side of the rule, that will batter the wall exactly 
right. The error of building walls plumb outside, is frequently committed in 
' building the abutments of bridges; the consequence is, they fall down in a short 
time; because the earth between the walls i* expanded a little by every hard 
frost, which forces the w r alls over. 

14 


210 


ON BUILDING MILL-WALLS. 


[CHAP. VIII. 


3. Use good mortar, and it will, in time, become as 
hard as stone.* 

4. Arch over all the windows, doors, &c. 

5. Tie them well together by the timbers of the floors. 

* Good mortar, made of pure, well burnt limestone, properly made up with 
sharp clean sand, free from any sort of earth, loam or mud, will, in time, actu¬ 
ally petrify, and turn to the consistence of a stone. It is better to put too much 
sand into your mortar than too little. Workmen choose their mortar rich, be¬ 
cause it works pleasantly; but rich mortar will not stand the weather so well, 
nor grow so hard as poor mortar. If it were all lime, it would have little more 
strength than clay. 





* ¥ 






CHAP. IX.] 


DESCRIPTION, ETC. 


211 


|5nrt lljr C'ljirfr. 


CHAPTER IX. 

DESCRIPTION OF THE AUTHOR’S IMPROVEMENTS IN THE MACHI¬ 
NERY FOR MANUFACTURING GRAIN INTO MEAL AND FLOUR. 


ARTICLE 87. 

INTRODUCTORY REMARKS. 

These improvements consist of the invention and ap¬ 
plication of the following machines, namely :— 

1. The Elevator. 

2. The Conveyer. 

3. The Hopper-boy. 

4. The Drill. 

5. The Descender. 

These five machines are variously applied in different 
mills, according to their construction, so as to perform 
every necessary movement of the grain and meal, from 
one part of the mill to another, or from one machine to 
another, through all the various operations from the 
time the grain is emptied from the wagoner’s bag, or 
from the measure on board the ship, until it be com¬ 
pletely manufactured into flour, either superfine or of 
other qualities, and separated, ready for packing into 
barrels, for sale or exportation. All of which is per¬ 
formed by the force of the water, without the aid of ma¬ 
nual labour, excepting to set the different machines in 
motion, &c. This lessens the labour and expense of at¬ 
tendance of flour mills, fully one-lialf. The whole, as 
applied, is represented in Plate VIII. 



212 


ELEVATOR AND CONVEYER. [CHAP. IX. 


ARTICLE 88. 

1. OF TIIE ELEVATOR. 

The elevator is an endless strap, revolving over two 
pulleys; one of which is situated at the place whence 
the grain or meal is to be hoisted, and the other where 
it is to be delivered; to this strap is fastened a number 
of small buckets, which fill themselves as they pass un¬ 
der the lower pulley, and empty themselves as they 
pass over the upper one. To prevent any waste of what 
may spill out of these buckets, the strap, buckets, and 
pulleys are all enclosed, and work in tight cases, so that 
what spills will descend to the place from whence it 
was hoisted. AB, in fig. 1, Plate VI., is an elevator for 
raising grain, which is let in at A, and discharged at B, 
into the spouts leading to the different garners. Fig. 2 
is a perspective view of the strap, with different kinds 
of buckets, and the various modes of fastening them to 
the strap. 


2. OF THE CONVEYER. 

The conveyer KI, Plate VI., fig. 1, is an endless screw 
of two continued spirals, put in motion in a trough; the 
grain is let in at one end, and the screw drives it to the 
other, or collects it to the centre, as at y, to run into 
the elevator, (see Plate VIII., 37—30—4, and 44—45,) 
or it is let in at the middle, and conveyed each wav, 
as 15, 16, Plate VIII. 

Fig. 3, Plate VI., is a top view of the lower pulley of 
a meal elevator in its case, and a meal conveyer in its 
trough, for conveying meal from the stones into the ele¬ 
vator as fast as ground. This conveyer is an eight-sided 
shaft, set on all sides with small inclining boards, called 
flights, for conveying the meal from one end of the trough 
to the other; these flights are set in spirally, as shown by 
the dotted line; but the flights being set across the spiral 
line, the principle of the machine is changed from a 


\ 




CHAP. IX.] THE HOPPER-BOY. 213 

screw to that of a number of ploughs; which is found to 
answer better for conveying warm meal. 

Besides these conveying flights, there are others 
sometimes necessary, which are called lifters; and set 
with their broadsides foremost, to raise the meal from 
one side of the shaft, and let it fall on the other side to 
cool; these are only used where the meal is hot, and 
the conveyer short; there may be half as many of these 
as of the conveying flights. See 21—22, in Plate VIII., 
which is a conveyer, carrying the meal from three pairs 
of stones to the elevator, 23—24. 

3. OF THE HOPPER-BOY. 

Fig. 12, Plate VII., is a hopper-boy; which consists 
of a perpendicular shaft, A B having a slow motion, (not 
• above 4 revolutions in a minute,) carrying round with 
it the horizontal piece C D, which is called the arm; this, 
on the under side, is set full of small inclining boards, 
called flights; so as to gather the meal towards the cen¬ 
tre, or to spread it from the centre to that part of the 
arm which passes over the bolting hopper; at this part, 
one board is set broadside foremost, as E, (called the 
sweeper.) which drives the meal before it, and drops it 
into the hoppers HII, as the arms pass over them. The 
meal is generally let fall from the elevator, at the extre¬ 
mity of the arm, at D, where there is a sweejier, which 
drives the mill before it, trailing it in a circle the whole 
way round, so as to discharge nearly the whole of its 
load, by the time it returns to be loaded again: the 
flights then gather it towards the centre, from every part 
of the circle; which would not be the case, if the sweepers 
did not lay it round; but the meal would, in this case, be 
gathered from one side only of the circle. These sweepers 
are screwed on the back of the arm, so that they may be 
raised or lowered, in order to make them discharge sooner 
or later, as may be found necessary. 

The extreme flight at each end of the arms is put on 
with a screw, passing through its centre, so that they may 
be turned to drive the meal outwards; the use of which 
is, to spread the warm meal as it falls from the elevator. 


214 


THE DRILL. 


[CIIAP. IX. 

in a ring, round the hopper-boy, while it, at the same 
time, gathers the cooled meal into the bolting hopper; 
so that the cold meal may be bolted, and the warm meal 
spread to cool, by the same machine, at the same time, 
if the miller chooses so to do. The foremost edge of the 
arm is sloped up in order to make it rise over the meal, 
and its weight is nearly balanced by the weight w, hung 
to one end of a cord, passing over the pulley P, and to 
the stay iron F. About 4 \ feet of the lower end of the 
upright shaft is made round, passing loosely through a 
round hole in the flight arm, giving it liberty to rise and 
fall freely, to suit any quantity of meal under it. The 
flight arm is led round by the leading arm L M, there 
being a cord passed through the holes L M, at each end, 
and made fast to the flight arm D C. This cord is length¬ 
ened or shortened by a hitch stick N, with two holes for 
the cord to pass through, its end being passed through a 
hole at D, and fastened to the end of a stick; this cord 
must reeve freely through the holes at the end of the 
arms, in order that the ends may both be led equally. 
The flight arm falls behind the leader about l-6th part 
of the circle. The stay-iron C F E, is formed into a 
ring at F, which fits the shaft loosely, keeps the arm 
steady, and serves for hanging the hands of an equal 
height, by means of the screws C E. 

Fig. 13, Plate VII., is a perspective view of the under 
side of the flight arms. The arm a c, with flights and 
sweepers complete; s s s show the screws which fasten 
the sweepers to the arms. The arm c b, is to show the 
rule for laying out for the flights. When the sweeper 
at b is turned in the position of the dotted line, it drives 
the meal outwards. Fig. 14, Plate VII., represents a 
plate of metal on the bottom of the shaft, to keep the 
arm from the floor, and 15 is the step gudgeon. 

4. OF THE DRILL. 

The drill is an endless strap revolving over two pul¬ 
leys, like an elevator, but set nearly horizontal, and, in¬ 
stead of buckets, there are small rakes fixed to the strap, 
which draw the grain or meal along the bottom of the 


CHAP. IX.] THE DESCENDER. 215 

case. See GII ? plate VI., fig. 1. The grain is let in 
at H, and discharged at G. This can sometimes be ap¬ 
plied at less expense than a conveyer; it should be set 
a little descending; it will move grain or meal with ease, 
and will answer well, even when a little ascending. 

5. OF THE DESCENDER. 

The descender is a broad, endless strap of very thin 
pliant leather, canvass, flannel, &c., revolving over two 
pulleys, which turn on small pivots, in a case or trough, 
to prevent waste, one end of which is to be lower than 
the other. See E F, Plate VI. fig. 1. The grain or 
meal falls from the elevator on the upper strap at E; 
and by its own gravity and fall sets the machine in mo¬ 
tion, which discharges the load over the lower pulley F. 
There are two small buckets to bring up what may spill 
or fall off the strap, and lodge in the bottom of the case. 

This machine moves on the principle of an overshot 
water-wheel, and will convey meal to a considerable 
distance, with a small descent. Where a motion can 
be readily obtained from the water, it is to be preferred, 
as when working by itself, it is easily stopped, and is 
apt to be troublesome. 

The crane spout is hung on a shaft to turn on pivots 
or a pin, so that it may turn every way, like a crane; 
into this spout the grain falls from the elevator, and it 
can be directed by it into any garner. The spout is 
made to fit close, and play under a broad board, and the 
grain is let into it through the middle of this board, 
near the pin; it will then always enter the spout. It 
is seen under B, Plate VI., fig. 1. L is a view of the 
under side of it, and M is a top view of it. The pin or 
shaft may reach down so low, that a man may stand on 
the floor and turn it by the handle x. 


21G APPLICATION OF THE MACHINES. [CHAP. X. 


CHAPTER X. 
ARTICLE 89. 


APPLICATION OF THE FOREGOING MACHINES IN THE PROCESS OF MA¬ 
NUFACTURING WHEAT INTO SUPERFINE FLOUR. 

Plate YIII. is not meant to show the plan of a mill, 
but merely the application and use of the foregoing ma¬ 
chines. 

The grain is emptied from the wagon into the spout 

1, which is set in the wall, and conveys it into the scale 

2, that is made to hold 10, 20, 30, or GO bushels, at 
pleasure. 

There should, for the convenience of counting, be 
weights of 60 lbs. each, divided into 30, 15, 71 lbs.; 
then each large weight would show a bushel of wheat, 
and the smaller ones halves, pecks, &c., which any one 
could count with ease. 

When the wheat is weighed, draw the gate at the 
bottom of the scale, and let it run into the garner 3; at 
the bottom of which there is a gate to let it into the ele¬ 
vator 4—5, which raises it to 5; the crane spout is to 
be turned over the great store garner G, which commu¬ 
nicates from floor to floor, to garner 7, over the stones 8, 
which may be intended for shelling or rubbing the wheat, 
before it is ground, to take off all dust that sticks to the 
grain, or to break smut, fly-eaten grain, lumps of dust, 
&c. As it is rubbed, it runs into 3 again: in its passage 
it goes through a current of wind, blowing into the tight 
room 9, having only the spout a, through the lower floor, 
for the wind to escape; all the chaff will settle in the 
room, but most of the dust will pass out with the wind at 
a. The wheat again runs into the elevator, at 4, and the 
crane spout, at 5, is turned over the screen hoppers 10 
or 11, and the grain lodged there, out of which it runs 
into the rolling screen 12, and descends through the cur¬ 
rent of wind made by the fan 13; the clean heavy grain 
descends, by 14, into the conveyer 15—1G, which con- 



217 


CHAP. X.] APPLICATION OF THE MACHINES. 

veys it into all the garners over the stones 7—17—18, 
and these regularly supply the stones 8—19—20, keep¬ 
ing always an equal quantity in the hoppers, which will 
cause them to feed regularly: as it is ground, the meal 
falls to the conveyer 21—22, which collects it to the 
meal elevator at 23, and it is raised to 24, whence it gent¬ 
ly runs down the spout to the hopper-boy at 25, which 
spreads and cools it sufficiently, and gathers it into the 
bolting hoppers, both of which it attends regularly; as it 
passes through the superfine cloths 26, the superfine 
Hour falls into the packing chest 28, which is on the se¬ 
cond floor. If the flour is to be loaded on wagons, it 
should be packed on this floor, that it may conveniently 
be rolled into them; but if the flour is to be put on 
board a vessel, it will be more convenient to pack on 
the lower floor, out of chest 29, and thence roll it into 
the vessel at 30. The shorts and bran should be kept 
on the second floor, that they may be conveyed by 
spouts into the vessel’s hold, to save labour. 

The rubbings which fall from the tail of the 1st reel 
26, are guided into the head of the 2d reel 27; which is 
in the same chest, near the floor, to save both room and 
machinery. On the head of this reel is 6 or 7 feet of 
fine cloth, for tail flour; and next to it the middling 
stuff, &c. 

The tail flour which falls from the tail of the 1st reel 
26, and head of the 2d reel 27, and requires to be bolted 
over again, is guided by a spout, as shown by dotted line 
21—22, into the conveyer 22—23, to be hoisted again 
with the ground meal; a little bran may be let in with 
it, to keep the cloth open in warm weather; but if there 
be not a fall sufficient for the tail flour to run into the 
lower conveyer, there may be one set to convey it into 
the elevator, as 31—32. There is a little regulating 
board, turning on the joint x, under the tail of the first 
reels to guide more or less with the tail flour. 

The middlings, as they fall, are conveyed into the eye 
of either pair of mill-stones by the conveyer 31—32, and 
ground over with the wheat; this is the best way of 
grinding them, because the grain keeps them from being 



218 APPICATION OF THE MACHINES. [CHAP. X. 

killed; there is no time lost in doing it, and they are re¬ 
gularly mixed with the flour. There is a sliding board 
set slanting, to guide the middlings over the conveyer, 
that the miller may take only such part for grinding over 
as he shall judge fit: a little regulating board stands be¬ 
tween the tail flour and middlings, to guide more or 
less into the stones or elevator. 

The light grains of wheat, screenings, &c., after being 
blown by the fan 13, fall into the screenings garner, 32; 
the chaff' is driven farther on, and settles in the chaff- 
room 33; the greater part of the dust will be carried 
out with the wind through the wall. For the theory 
of fanning wheat, see Art. S3. :i: 


To clean the screenings. 

Draw the little gate 34, and let them into the eleva¬ 
tor at 4, to be elevated into garner 10; then draw gate 10, 
and shut 11 and 34, and let them pass through the roll¬ 
ing screen 12, and fan 13; and as they fall at 14, guide 
them down a spout (shown by dotted lines) into the ele¬ 
vator at 4, and elevate them into the screen-hopper 11; 
then draw gate 11, shut 10, and let them take the same 
course over again, and return into the garner 10, &c., as 
often as necessary: when cleaned, guide them into the 
stones to be ground. 

The screenings of the screenings are now in garner 
32, which may be cleaned as before, and an inferior 
quality of meal made out of them. 

By these means the wheat may be effectually sepa¬ 
rated from the seed of weeds, &c., and these saved for 
food for cattle. 

This completes the whole process from the wagon to 
the wagon again, without manual labour, except in pack¬ 
ing the flour and rolling it in. 


* The bolting reels may all be set in a line connected by jointed gudgeons, 
supported by bearers. The meal, as it leaves the tail of one reel, may be intro¬ 
duced into the head of the other, by an elevator bucket, fixed on the head of the 
reel open at the side next the centre, so that it will dip up the meal, and, as it 
passes over the centre, drop it in. This improvement was made by Mr. Jona¬ 
than Ellicott; and by it, in many cases, many wheels and shafts, and much 
room may be saved. 


CnAP. X.] APPLICATION OF THE MACHINES. 219 


ARTICLE 90. 

OF ELEVATING GRAIN FROM SHIFS. 

If the grain come to the mill by ships, No. 35, and 
require to be measured at the mill, then a conveyer, 35 
—4, may be set in motion by the great cog-wheel, and 
may he under or above the lower floor, as may best suit 
the height of the floor above high water. This conveyer 
must have a joint, as 36, in the middle, to give the end 
that lies on the side of the ship, liberty to raise and lower 
with the tide. The wheat, as measured, is poured into 
the hopper at 35, and is conveyed into the elevator at 4; 
which conveyer will so rub the grain as to answer the 
end of rubbing stones. And in order to blow away the 
dust, when rubbed off, before it enters the elevator, part 
of the wind made by the fan 13, may be brought down 
by a spout, 13—36, and when it enters the case of the 
conveyer, it will pass each way, and blow out the dust 
at 37 and 4. 

In some instances, a short elevator may be used, with 
the centre of the upper pulley, 38, fixed immovably, 
the other end resting on the deck, but so much aslant as 
to give the vessel liberty to raise and lower: the elevator 
will then slide a little on the deck. The case of the 
lower strap of this elevator must be considerably crook¬ 
ed, to prevent the points of the bucket from wearing 
by rubbing in their descent. The wheat, as measured, 
is poured into a hopper, which lets it in at the bottom 
of the pulley. 

But if the grain is not to be measured at the mill, 
then fix the elevator 35—39, to take it out of the hold, 
and elevate it through any conveniently situated door. 
The upper pulley is fixed in a gate that plays up and 
down in circular rabbets, to raise and lower to suit the 
tide and depth of the hold, and to reach the wheat. 
40 is a draft of the gate, and manner of hanging the 
elevator in it. (See particular description thereof, in 
the latter part of Article 95.) 

This gate is hung by a stout rope, passing over a 



220 


APPLICATION OF THE MACHINES. [CHAP. X. 

strong pulley or roller 41, and thence round the axis of 
the wheel 42, round the rim of which wheel there is a 
rope, which passes round the axis of the wheel 43, round 
the rim of which is a small rope, leading down over the 
pulley P, to the deck, and fastened to the cleet q: a man, 
by pulling this rope, can hoist the whole elevator; be¬ 
cause, if the diameter of the axis be 1 foot, and the wheel 
4 feet, the power is increased 1G fold. The elevator 
is hoisted up, and rested against the wall, until the ship 
comes to, and is fastened steadily in the right place; then 
it is set in the hold on the top of the wheat, and the bot¬ 
tom being open, the buckets fill as they pass under the 
pulley; a man holds by the cord, and lets the elevator 
settle as the wheat sinks in the hold, until the lower 
part of the case rests on the bottom of the hold, it being 
so long as to keep the buckets from touching the vessel; 
by this time it will have hoisted 1, 2, or 300 bushels, ac¬ 
cording to the size of the ship and depth of the hold, at 
the rate of 300 bushels per hour. When the grain 
ceases running in of itself, the man may shovel it up, 
till the load is discharged. 

The elevator discharges the wheat into the conveyer 
at 44, which conveys it into the screen-hoppers 10—11, 
or into any other, from which it may descend into the 
elevator 4—5, or into the rubbing stones 8. 

This conveyer may serve instead of rubbing stones, 
and the dust rubbed off thereby may be blown out 
through the wall at p, by a wind spout from fan 13, into 
the conveyer at 45. The holes at 44 and 10—11, are 
to be small, to let but little wind escape any where, ex¬ 
cepting through the wall, where it will cary off the dust. 

A small quantity of wind might be let into the con¬ 
veyer 15—16, to blow away the dust rubbed oft'by it. 

The fan, to be sufficient for all these purposes, must 
be made to blow very strongly, and the strength of the 
blast may be regulated as directed by Art. 83. 




CHAP. X.] APPLICATION OF THE MACHINES. 


221 


ARTICLE 91. 

A MILL FOR GRINDING PARCELS. 

Here each person’s parcel is to be stored in a separate 
garner, and kept separate through the whole process of 
manufacture, which occasions much labour; almost all 
of which is performed by the machines. See Plate VI., 
fig-1; which is a view of one side of the mill, containing 
a number of garners holding parcels, and a side view of 
the wheat elevator. 

The grain is emptied into the garner g,from the wagon, 
as shown in Plate VIII., and, by drawing the gate A, it 
is let into the elevator A B, and elevated into the crane- 
spout B, which, being turned into the mouth of the gar¬ 
ner-spout B C, which leads over the top of a number of 
garners, and has, in its bottom, a little gate over each 
garner; these gates and garners are all numbered with 
the same numbers, respectively. 

Suppose we wish to deposite the grain in the garner 
No. 2, draw the gate 3 out of the bottom, and shut it in 
the spout: to stop the wheat from passing along it, pass 
the hole, so that it must all fall into the garner; and 
thus proceed for the other garners 3 4 5 6, &c. These 
garners are all made like hoppers, about four inches wide 
at the floor, and nearly the length of the garner; but as 
it passes through the next story, it is brought to the form 
of a spout, 4 inches square, leading down to the general 
spout K A, which leads to the elevator: in each of these 
spouts is a gate numbered with the number of its gamer, 
so that when we want to grind the parcel in garner 2, we 
draw the gate 2 in the lower spout, to let the wheat run 
into the elevator at A, to be elevated into the crane-spout 
B, which is to be turned over the rolling-screen, as shown 
in Plate VIII. 

Under the upper tier of garners, there is another tier 
in the next story, set so that the spouts from the bottom 
of the upper tier pass down the partitions of the lower 
tier, and the upper spouts of the lower tier pass between 
the partitions of the upper tier, to the garner-spout. 


222 APPLICATION OF TIIE MACHINES. [CHAP. X. 

These garners, and the gates leading both into and 
out of them, are numbered as the others. 

If it be not convenient to fix the descending spouts 
B C, to convey the wheat from the elevator to the gar¬ 
ners, and K A to convey it from the garners to the ele¬ 
vator again, then the conveyers r s and I K may be used 
for said purposes. 

To keep the parcels separate, there should be a crane- 
spout to the meal elevator; or any other method may be 
adopted, by which the meal of the second parcel may be 
guided to fall on another part of the floor, until the first 
parcel is all bolted, and the chests cleared out, when the 
meal of the second parcel may be guided into the hop¬ 
per-boy. 

I must here observe, that in mills for grinding parcels 
the tail flour must be hoisted by a separate elevator to 
the hopper-boy, to be bolted over; and not run into the 
conveyer, as shown in Plate VIII.; because then the par¬ 
cels could not be kept separate. 

The advantages of the machinery, applied to a mill 
for grinding parcels, are very great. 

1. Because without them there is much labour in 
moving the different parcels from place to place: all 
which is here done by the machinery. 

2. The meal as it is ground, is cooled by the machi¬ 
nery, and bolted in so short a time, that, when the grind¬ 
ing is done, the bolting is also nearly finished. There¬ 
fore, 

3. It saves room, because the meal need not be spread 
over the floor to cool, during 12 hours, as is usual; and 
but one parcel need be on the floor at one time. 

4. It gives greater despatch, as the miller need never 
stop either stones or bolts, in order to keep parcels se¬ 
parate. The screenings of each parcel may be cleaned, 
as directed in Art. 89, with very little trouble; and the 
flour may be nearly packed before the grinding is 
finished; so that if a parcel of 60 bushels arrive at the 
mill in the evening, the owner may wait till morning, 
when he may have it all finished; he may use the offal for 
feed for his team, and proceed with his load to market. 


CHAP. X.] APPLICATION OF THE MACHINES. 


99 Q 


ARTICLE 92. 

A GRIST-MILL FOR GRINDING VERY SMALL PARCELS. 

Fig. 16, Plate VII., is a representation of a grist-mill, 
so constructed that the grist being put into the hopper, 
it will be ground and bolted and returned into the bags 
again. 

The grain is emptied into the hopper at A, and as it 
is ground it runs into the elevator at B, and is elevated 
and let run into the bolting hopper down a board spout 
at C, and, as bolted, it falls into the bags at d. The chest 
is made to come to a point like a funnel, and a division 
made to separate the tine and coarse, if wanted, and a 
bag put under each jiart; on the top of this division is 
set a regulating board on a joint, as x, by which the tine 
and coarse can be regulated at pleasure. 

If the bran require to be ground over, (as it often 
does,) it is made to fall into a box over the hopper, and 
by drawing the little gate b, it may be let into the hop¬ 
per as soon as the grain is all ground, and as it is bolted 
the second time, it is let run into the bag by shutting the 
gate b, and drawing the gate c. 

If the grain be put into the hopper F, then as it is 
ground it falls into the drill, which draws it into the ele¬ 
vator at B, and it ascends as before. 

To keep the different grists separate;—when the 
miller sees the first grist fall into the elevator, he shuts 
the gate B or d, and gives time for it all to get into the 
bolting reel; he then stops the knocking of the shoe by 
pulling the shoe line, which hangs over the pulleys p p, 
from the shoe to near his hand, making it fast to a peg; 
he then draws the gate B or d, and lets the second grist 
into the elevator, to fall into the shoe or bolting hopper, 
giving time for the first grist to be all in the bags, and 
the bags of the second grist to be put in their places; he 
then unhitches the line from the peg, and lets the shoe 
knock again; and begins to bolt the second grist. 

If he does not choose to let the meal run immediately 
into the bags, lie may have a box made with feet, to stand 


224 APPLICATION OF TIIE MACHINES. [CHAP. X. 

in the place of the bags, for the meal to fall in, out of 
which it may be taken and put into the bags, as fast as 
it is bolted, and mixed as desired; and as soon as the 
first parcel is bolted, the little gates at the mouth of the 
bags may be shut, while the meal is filled out of the 
box, and the second grist may be bolting. 

The advantages of this improvement on a grist-mill 
are, 

1. It saves the labour of hoisting, spreading, and cool¬ 
ing the meal, and of carrying up the bran to be ground 
over, sweeping the chest, and filling up the bags. 

2. It does all with great despatch, and little waste, 
without having to stop the stones or bolting-reel, to keep 
the grist separate, and the bolting is finished almost as 
soon as the grinding; therefore, the owner will be the 
less time detained. 

The chests and spouts should be made steep, to pre¬ 
vent the meal from lodging in them; so that the miller, 
by striking the bottom of the chest, will shake out all 
the meal. 

The elevator and drill should be so made as to clean 
out at one revolution. The drill might have a brush or 
two, instead of rakes, which would sweep the case clean 
at a revolution; and the shoe of the bolting hopper 
should be short and steep, so that it will clean out ra- 
pidly. . • • ■ 

The same machinery may be used for merchant-work, 
by having a crane-spout at C; or a small gate, to turn the 
meal into the hopper-boy that tends the merchant bolt. 

A mill, thus constructed, might grind grists in the 
day-time, and merchant-work at night. 

A drill is preferable to a conveyer for grist-mills, be¬ 
cause it may be cleaned out much sooner and better. The 
lower pulley of the elevator is twice as large in diameter 
as the pulleys of the drill; the lower pullej^ of the ele¬ 
vator, and one pulley of the drill, are on the same shaft, 
close together; the elevator moves the drill, and the pul¬ 
ley of the drill being smallest, gives room for the meal 
to fall into the buckets of the elevator. 


CHAP. X.] APPLICATION OF TnE MACHINES. 


225 


ARTICLE 93. 

OF ELEVATING GRAIN, SALT, OR ANY GRANULAR SUBSTANCE FROM 
SHIPS INTO STORE-HOUSES, BY THE STRENGTH OF A nORSE. 

Plate VII., fig. 17, represents the elevator and the 
manner of giving it motion; the horse is hitched to the 
end of the sweep-beam A, by which he turns the upright 
shaft, on the top of which is the driving cog-wheel of 96 
cogs 21 inches pitch, to gear into the leading wheel of 20 
cogs, on the same shaft with which is another driving- 
wheel of 40 cogs, to gear into another leading wheel of 
19 cogs, which is on the same shaft with the elevator 
pulley; then, if the horse make about 3 revolutions in a 
minute, (which he will do if he walk in a circle of 20 feet 
diameter,) the elevator pulley will make about 30 revo¬ 
lutions in a minute; and if the pulley be 2 feet in diame¬ 
ter, and a bucket be put on every foot of the strap, to 
hold a quart each, the elevator will hoist about 187 
quarts per minute, or 320 bushels in an hour; 3840 
bushels in 12hours; and for every foot the elevator is 
high, the horse will have to sustain the weight of a 
quart of wheat, say 48 feet, which is the height of the 
highest store-houses, then the horse would have to move 
1£ bushels of wheat upwards, with a velocity equal to 
his own wmlk; which, I presume, he can do with ease, 
and overcome the friction of the machinery. From this 
will appear the great advantages of this application. 

The lower end of the elevator should stand near the 
side of the ship, and the grain, salt, &c., be emptied into 
a hopper; the upper end may pass through a door or 
window, as may be most convenient: the lower case 
should be a little crooked to prevent the buckets from 
rubbing in their descent. 


15 


226 APPLICATION OF THE MACHINES. [CHAP. X. 


ARTICLE 94. 

OF AN ELEVATOR APPLIED TO ELEVATE GRAIN, ETC., WROUGHT BY A 

MAN. 

In Plate VII., fig. 18, A B, are two racket wheels, 
with two deep grooves in each of them, for ropes to run 
in; they are fixed close together, on the same shaft with 
the upper pulley of the elevator, so that they will turn 
easily on the shaft the backward way, whilst a click falls 
into the racket and prevents them from turning for¬ 
wards. Fig. 19 is a side view of the wheel, racket, and 
click. C D are two levers, like weavers’ treadles, and 
from lever C there is a light staff parses to the foreside of 
the groove wheel B, and is made fast by a rope half way 
round the wheel; and from said lever C there is a rope 
passing to the backside of the wheel A; and from lever. 
D there is a light staff passing to the foreside of the 
groove wheel A, and a rope to the backside of the 
groove wheel B. 

The man who is to work this machine stands on the 
treadles, and holds by the staff with his hands; and as 
he treads on D it descends, and the staff pulls the wheel 
A forward, and the rope pulls the wheel B backward, 
and as he treads on C, the staff pulls forward the wheel 
B, and the rope pulls backward the wheel A; but the 
click falls into the racket, so that the wheels cannot 
move forward without turning the elevator pulley: it is 
thus moved oneway by both treadles; and in order to 
keep up a regular motion, a heavy flying wheel F, is 
added, which should be of cast iron, to prevent much 
obstruction from the air. 

To calculate what quantity a man can raise to any 
height, let us suppose his weight to be 150 lbs., which is 
the power to be applied; and suppose he be able to walk 
about 70 feet up stairs in minute, by the strength of 
both his legs and arms, or, which is the same thing, to 
move his weight on the treadles 70 steps in a minute: 
then, suppose we allow, as by Art. 29—42, to lose l-3d 
of the power to gain velocity and overcome friction, 
(which will be a large allowance in this case, because in 



227 


CHAP. X.] APPLICATION OF THE MACHINES. 

the experiment in the table, in Art. 37, when 7 lbs. were 
charged with 6 lbs. they moved with the velocity of 2 
feet in half a second,) then there will remain 100 lbs. 
raised 70 feet in a minute, ecpial to 200 lbs. raised 35 feet, 
to the top of the third story, per minute, equal to 200 
bushels per hour, 2400 bushels in twelve hours. 

The great advantages of this application of the eleva¬ 
tor, and of this mode of applying man’s strength, will 
appear from these considerations, namely: he uses the 
strength of both his legs and arms, to move his weight 
only from one treadle to the other, which weight does the 
work; whereas, in carrying bags on his back, he uses the 
strength of his legs only, to raise both the weight of his 
body and the burden; add to this, that he generally takes 
a very circuitous route to the place where he is to empty 
the bag, and returns empty; whereas, the elevator takes 
the shortest direction to the place of emptying, and is 
always steadily at work. 

The man must sit on a high bench, as a weaver does, 
on which he can rest part of his weight, and rest himsell 
occasionally, when the machine moves lightly, and have 
a beam above, that he may push his head against, to 
overcome extraordinary resistances. This is probably 
the best means of applying man’s strength to produce 
rotary motion. 

DESCRIPTION OF PLATE IX. 

The grain is emptied into the spout A, by which it 
descends into the garner B; whence, by drawing the gate 
at C, it passes into the elevator C D, which raises it to IX 
and empties it into the crane spout E, which is so fixed 
on gudgeons that it may be turned to any of the surround¬ 
ing garners, into the screen hopper F, for instance, (which 
has two parts F and G,) out of which it is let into the roll¬ 
ing screen at H, by drawing the small gate a. It passes 
through the fan I, and falls into the little sliding-hopper 
K, which may be moved, so as to guide it into either of 
the hanging garners, over the stones, L or M, and it is 
let into the stone-hoppers by the little bags b b, as fast 
as it can be ground. When ground, it falls into the con- 


228 APPLICATION OF THE MACHINES. [CHAP. X. 

veyor N N, which carries it into the elevator at 0 0, 
this raises and empties it into the hopper-boy at P, 
which is so constructed as to carry it round in a ring, 
gathering it gradually towards the centre, till it sweeps 
into the bolting hoppers Q Q. 

The tail flour, as it falls, is guided into the elevator to 
ascend with the meal, and, that a proper quantity may 
be elevated, there is a regulating board R, set under the 
superfine cloths, on a joint x, so that it will turn towards 
the head or tail of the reel, and send more or less into 
the elevator, as may be required. 

There may be a piece of coarse cloth, or wire, put on 
the tails of the superfine reels, that will let all pass 
through except the bran which falls out at the tail, and 
a part of which is guided into the elevator with the tail 
flour, to assist the bolting in warm weather; the quan¬ 
tity is regulated by a small board r, set on a joint under 
the ends of the reels. Beans may be used to keep the 
cloths open, and still be returned into the elevator to 
ascend again. What passes through the coarse cloth or 
wire and the remainder of the bran, are guided into the 
reel S, to be bolted. 

To clean Wheat several times . 

Suppose the grain to be in the screen hopper E; draw 
the gate a; shut the gate e; move the sliding hopper K, 
over the spout K c d; and let it run into the elevator to 
be raised again. Turn the crane spout over the empty 
hopper G, and the wheat will be all deposited there 
nearly as soon as it is out of the hopper F. Then draw 
the gate e, shut the gate a, and turn the crane spout 
over F; and so on, alternately, as often as necessary. 
When the grain is sufficiently cleaned, slide the hopper 
K over the hole that leads into the stones. 

The screenings fall into a garner, hopperwise; to clean 
them, draw the gate f, and let them run into the eleva¬ 
tor, to be elevated into the screen hopper F. Then pro¬ 
ceed with them as with the wheat, till sufficiently clean. 
To clean the fannings, draw the little gate h, and let 
them into the elevator, &c., as before. 


229 


CHAP. XI.] CONSTRUCTION OP MACHINES. 

Fig. II. is a jDerspective view of the conveyer, as it lies 
in its troughs, at work; and shows the manner in which 
. it is joined to the pulleys, at each side of the elevator. 

Fig. III. exhibits a view of the pulley of the meal ele¬ 
vator, as it is supported on each side, with the strap and 
buckets descending to be filled. 

Fig. IV. is a perspective view of the under side of the 
arms of the hopper-boy, with flights complete. The 
dotted line shows the track of the flights of one arm; 
those of the other following, and tracking between them. 
A A are the sweepers. These carry the meal round in 
a ring, trailing it regularly all the way, the flights draw¬ 
ing it to the centre, as already mentioned. B B are the 
sweepers that drive it into the bolting hoppers. 

Fig. V. is a perspective view of the bucket of the 
wheat-elevator; and shows the manner in which it is 
fastened, by a broad piece of leather, which passes 
through and under the elevator strap, and is nailed to 
the sides with little tacks. 


CHAPTER XI. 

OF THE CONSTRUCTION OF THE SEVERAL MACHINES. 

ARTICLE 95. 

OF THE WHEAT ELEVATOR. 

To construct a wheat-elevator, first determine how 
many bushels it should hoist in an hour, and where it 
shall be set, so as, if possible, to answer all the following- 
purposes :— 

1. To elevate the grain from a wagon or ship. 

2. From the different garners into which it may be 

stored. 

3. If it be a two-story mill to hoist the wheat from 
the tail of the fan, as it is cleaned, to a garner over the 
stones. 



230 CONSTRUCTION OF MACHINES. [CHAP. XI. 

4. To hoist the screenings, to clean them several 
times. 

5. To hoist the wheat from a shelling-mill, if there be* 
one. 

One elevator may effect all these objects in a mill 
rightly planned, and most of them can be accomplished 
in mills ready built. 

Suppose it be wished to hoist about 300 bushels in an 
hour, make the strap 4 2 inches wide, of good, strong, 
white harness leather, in one thickness. It must be cut 
and joined together in a straight line, with the thickest, 
and, consequently, the thinnest ends together, so that if 
they be too thin, they may be lapped over and doubled, 
until they are thick enough singly. Then, to make 
wooden buckets, take the but of a willow or water birch, 
that will split freely; cut it in bolts 15 inches long, and 
rive and shave it into staves, inches wide, and three- 
eighths of an inch thick; these will make 1 bucket each. 
Set a pair of compasses to the width of the strap, and 
make the sides and middle of the bucket equal thereto at 
the mouth, but let the sides be only two-tliirds of that 
width at the bottom, which will make it of the form of 
fig. 9, Plate VI.; the ends being cut a little circular, to 
make the buckets lie more closely to the strap and wheel, 
as it passes over. Make a pattern of the form of fig. 9, 
by which to describe all the rest. This makes a bucket 
of a neat form, to hold about 75 solid inches, or somewhat 
more than a quart. To make them bend to a square at 
the corners e c, cut a mitre square across where they are 
to bend, about 2-8ths through; boil them, and bend them 
hot, tacking a strip of leather across them, to hold them 
in that form until they get cold, and then put bottoms to 
them of the thin skirts of the harness leather. These 
bottoms are to extend from the lower end to the strap 
that binds it on. To fasten them on well, and with de¬ 
spatch, prepare a number of straps, 1| inch wide, of 
the best cuttings of the harness leather; wet them and 
stretch them as hard as possible, which reduces their 
width to about inches. Nail one of these straps to 
the side of a bucket, with 5 or 6 strong tacks that will 
reach through the bucket, and clinch inside. Then take 
a li inch chisel, and strike it through the main strap 


231 


CIIAP. XI.] CONSTRUCTION OF MACHINES. 

about a quarter of an inch from each edge, and put one 
end of the binding-strap through the slits, draw the 
bucket very closely to the strap, and nail it on the other 
side of the bucket, which will finish it. See B in fig. 2. 
Plate YI. C is a meal-bucket fastened in the same man¬ 
ner, but is bottomed only with leather at the lower end, 
the main strap making the bottom side of it. This is the 
best way I have yet discovered to make wooden buckets. 
The straps of the harness leather, out of which the ele¬ 
vator-straps are cut, are generally about enough to com¬ 
plete the buckets. 

To make Sheet-Iron Backets. 

Cut the sheet in the form of fig. 8, Plate YI., making 
the middle part, c, and the sides, a and b, nearly equal to 
the width of the strap, and nearly 5 i inches long, as be¬ 
fore. Bend them to a right angle at every dotted line, 
and the bucket will be formed:—c will be the bottom 
side next to the strap; and the little holes a a and b b 
will meet, and must be riveted to hold it together. The 
two holes c are for fastening it to the straps by rivets. 
The part a b is the part that dips up the wheat, and the 
point, being doubled back, strengthens it, and tends to 
make it wear well. The bucket being completely formed, 
and the rivet holes made, spread one out again, as fig. 
8, to describe all the rest by, and to mark for the holes, 
which will meet again when folded up. They are fas¬ 
tened to the strap by two rivets with thin heads, put in¬ 
side the bucket, and a double burr of sheet-iron put on 
the under side of the strap, which fastens them on very 
tightly. See A, fig. 2, Plate YI. These buckets will 
hold about 1.3 quarts or 88 cubic inches. This is the 
best way I have found to make sheet-iron buckets. D is 
a meal-bucket of sheet-iron, riveted on by two rivets, 
with their heads inside the strap; the sides of the buckets 
are turned a little out, and holes made in them, for the 
rivets to pass through. Fig. 11, is the form of one 
spread out, and the dotted lines show where they are 
to be bent at right angles to form them. The strap 
forms the bottom side of these buckets. 


232 CONSTRUCTION OF MACHINES. [CIIAP. XI. 

Make the pulleys 24 inches in diameter, as thick as 
the strap is wide, and half an inch higher in the middle 
than at the sides, to make the strap keep on; give them 
a motion of 25 revolutions in a minute, and put on a sheet 
iron bucket for every 15 inches: then 125 buckets will 
pass per minute, which will carry 162 quarts, and hoist 
300 bushels in an hour, and 3600 bushels in 12 hours. 

If you wish to hoist faster, make the strap wider, the 
buckets larger in proportion, and increase the velocity 
of the pulley, but not to above 35 revolutions in a minute, 
nor place more buckets than one for every 12 inches, 
otherwise they will not empty well. A strap of 5 inches, 
with buckets 6 inches long, and of a width and propor¬ 
tion suiting the strap, (4£ inches wide,) will hold 1.8 
quarts each; and 35 revolutions of the pulley will pass 
175 buckets, which will carry 315 quarts in a minute, 
and 590 bushels in an hour. If the strap be 4 inches 
wide, and the wooden buckets 5 inches deep, and, in pro¬ 
portion to the strap, they will hold .8 of a quart: then, 
if there be one for every 15 inches, and the pulley makes 
27 revolutions in a minute, it will hoist 200 bushels in 
an hour. Where there is a good garner to empty the 
wheat into, this is the size they are commonly made, 
and is sufficient for unloading wagons. 

Plate VI., Fig. 6, represents the gudgeon of the lower 
pulley, fig. 7, the gudeon for the shaft on which the 
upper pulley is fixed. Fix both the pulleys in their 
places, but not firmly, so that a line, stretched from one 
pulley to the other, will cross the shafts or gudgeons at 
right angles. This must always be the case to make the 
straps work fairly. Put on the strap with the buckets; 
draw it tightly, and buckle it; put it in motion, and if it 
do not keep fairly on the pulleys, their position may be 
altered a little. Observe how much the descending strap 
swags by the weight of the buckets, and make the case 
round it so curved, that the points of their buckets will 
not rub in their descent, which will cause them to wear 
long and work easily. The side boards need not be made 
crooked in dressing out, but may be bent sufficiently by 
sawing them half way, or two thirds through, beginning 


CHAP. XI.] CONSTRUCTION OF MACHINES. 233 

at the upper edge, holding the saw very much aslant, 
the point downwards and inwards, so that in bending, the 
parts will slip past each other. The upper case must be 
nearly straight; for if it be made much crooked, the 
buckets will incline to turn under the strap. Make the 
cases 3-4 ths of an inch wider inside than the strap and 
buckets, and lh inches deeper, that they may play free¬ 
ly; but do not give them room to turn upside down. If 
the strap and buckets be 4 inches, then make the side 
boards 5 2 , and the top and bottom boards 61 inches wide, 
of inch boards. Be careful that no shoulders nor nail- 
points be left inside of the cases, for the buckets to catch 
in. Make the ends of each case, where the buckets en¬ 
ter as they pass over the pulleys, a little wider than the 
rest of the case. Both the pulleys are to be nicely cased 
round to prevent waste, not leaving room for a grain to 
escape, continuing the case of the same width round the 
top of the upper, and bottom of the lower pulley; then if 
any of the buckets should ever get loose, and stand askew, 
they will be kept right by the case; whereas, if there 
were any ends of boards or shoulders, they would catch 
against them. See A B, fig. 1, Plate VI. The bottom 
of the case of the upper pulley must be descending, so 
that what grain may fall out of the buckets in passing 
over the pulleys, may be guided into the descending 
case. The shaft passing through this pulley is made 
round where the case fits to it: half circles are cut out 
of two boards, so that they meet and embrace it closely. 
The undermost board, where it meets the shaft, is ci¬ 
phered off inside next the pulley, to guide the grain in¬ 
ward. But it is full as good a way to have a strong 
gudgeon to pass through the upper pulley, with a tenon 
at one end, to enter a socket, which may be in the shaft, 
that is to give it motion. This will suit best where the 
shaft is short, and has to be moved to put the elevator 
out of, and into gear. 

The way that I have generally cased the pulleys is as 
follows, namely; the top board of the upper strap-case 
and the bottom board of the lower strap-case, are ex¬ 
tended past the lower pulley to rest on the floor; and the 


234 


CONSTRUCTION OF MACHINES. [CHAP XI. 

lower ends of these boards are made two inches narrower, 
as far as the pulley-case extends; the side-board of the 
pulley is nailed, or rather screwed, to them, with wooden 
screws. The rest of the case boards join to the top of 
the pulley-case, both being of one width. The block, 
which the gudgeons of this pulley run in, is screwed fast 
to the outside of the case boards; the gudgeons do not 
pass quite through, but reach to the bottom of the hole, 
which keeps the pulley in its place. 

The top and bottom boards, and, also, the side-boards 
of the strap cases, are extended past the upper pulley, 
and the side-boards of the pulley-case are screwed to 
them; but this leaves a vacancy between the top of the 
side-boards, of the strap-cases, and shoulders for the buck¬ 
ets to catch against, and this vacancy is to be filled up 
by a short board, guiding the buckets safely over the 
upper pulley. The case must be as close to the points 
of the buckets, where they empty, as is safe, that as 
little as possible may fall down again. There is to be 
a long hole cut into the case at B, for the wheat to fall 
out at, and a short spout guiding it into the crane spout. 
The top of the short spout next B, should be loosely 
fastened in with a button, that it may be taken off, to 
examine if the buckets empty well, &c. Some neat 
workmen have a much better way of casing the pulleys, 
which is not easily described: what I have described is 
the cheapest, and answers very well. 

The wheat should be let in at the bottom, to meet the 
buckets; and a gate should shut as near to the point of 
them as possible, as at A, fig. 1, Plate VI. Then, if 
the gate be drawn sufficiently to fill the buckets, and the 
elevator be stopped, the wheat will stop running in, and 
the elevator will be free to start again; but if it had been 
let in any distance up, then, when the elevator stopped, 
it would fill from the gate to the bottom of the pulley, 
and the elevator could not start again. If it be, in any 
case, let in at a greater distance up, the gate should be 
so fixed that it cannot be drawn so far as to let in the 
wheat faster than the buckets can take it, else the case 
will fill and stop the buckets. If it be let in faster at the 


235 


CHAP. XI.] CONSTRUCTION OF MACHINES. 

hindmost side of the pulley than the buckets will carry 
it, the same evil will occur; because the buckets will 
push the wheat before them, being more than they can 
hold, and give room for too much to come in; therefore, 
there should be a relief gate at the bottom, to let the 
wheat out, should too much happen to get in. 

The motion is to be given to the upper pulley of all 
elevators, if it can be done, because the weight in the 
buckets causes the strap to hang tightly on the upper, 
and slacker on the lower pulley; therefore, the upper 
pulley will carry the greatest quantity without slipping. 
All elevators should stand a little slanting, because they 
will discharge the better. The boards for the cases 
should be of unequal lengths, so that two joints may 
never come close together; this greatly strengthens the 
case. Some have joined the cases at every floor, which 
is a great error. There must be a door in the ascend¬ 
ing case, at the place most convenient for buckling the 
strap, &c. &c. 


Of the Crane-Spout. 

To make a crane-spout, fix a board 18 or 20 inches 
broad, truly horizontal, or level, as a, under B, in fig. 1, 
Plate YI. Through the middle of this board the wheat 
is conveyed, by a short spout, from the elevator. Then 
make the spout of 4 boards, 12 inches wide at the upper, 
and about 4 or 5 inches at the lower end. Cut the up¬ 
per end off' aslant, so as to fit nicely to the bottom of the 
board; hang it to a strong pin, passing through the broad 
board near the hole through which the wheat passes, so 
that the spout may be turned in any direction, and still 
cover the hole, at the same time it is receiving the wheat, 
and guiding it into any garner, at pleasure. In order 
that the pin may have a strong hold of the board and 
spout, there must be a piece of scantling, 4 inches thick, 
nailed on the top of the board, for the pin to pass through; 
and another to the bottom, for the head of the pin to rest 
on. But if the spout be long and heavy, it is best to 
hang it on a shaft, that may extend down to the floor, 
or below the collar-beams, with a pin through it, as x, 


236 


CONSTRUCTION OF MACHINES. [CHAP. XI. 

to turn the spout by. In crane-spouts for meal, it is 
sometimes best to let the lower board reach to, and rest 
on the floor. If the elevator cases and crane-spout be 
well fixed, there can neither grain nor meal escape, or 
be wasted, that enters the elevator, until it comes out 
at the end of the crane-spout again. 

Of an Elevator to elevate Wheat from a Ship’s Hold S' 

Make the elevator complete (as it appears 35—39, 
Plate VIII.) on the ground, and raise it to its place 
afterwards. The pulleys are to be both fixed in their 
places and cased; and the blocks that the gudgeon of 
the upper pulley is to run in, are to be riveted fast to 
the case-boards of the pulley, and these case-boards 
screwed to the strap-cases by long screws, reaching 
through the case-boards edgewise. Both sides of the 
pulley-case are fastened by one set of screws. On the 
outside of these blocks, round the centre of the gudgeons, 
are circular knobs, 6 inches diameter, and 3 inches long, 
strongly riveted to keep them from splitting off, because, 
by these knobs the whole weight of the elevator is to 
hang. In the moveable frame 40, o o, o o, are these 
blocks with their knobs, which are let into the pieces of 
the frame B G r s. The gudgeons of the upper pulley 
p pass through these knobs and play in them. Their 
use is to bear the weight of the elevator that hangs by 
them; the gudgeons, by this means, bear only the weight 
of the strap and its load, as is the case with other ele¬ 
vators. Tlieir being circular, gives the elevator liberty 
to swing out from the wall to the hold of the ship. 

The frame 40 is made as follows: the top piece A B is 
9 by 8 inches, strongly tenoned into the side pieces AI) 
and B G with double tenons, which side pieces are 8 by 
6. The piece r s is put in with a tenon, 3 inches thick, 
which is dove-tailed, keyed, and draw-pinned, with an 
iron pin, so that it can be easily taken out. In each 
side piece A D and B G there is a row of cogs, set in a 
circle, that are to play in circular rabbets in the posts 


* See the description of this elevator in Art. 90. 


237 


CHAP. XI.] CONSTRUCTION OF MACHINES. 

%>. 41. These circles are to be described with a radius, 
whose length is from the centre of the joint gudgeon G, 
to the centre of the pulley 39; and the post must be set 
up, so that the centre of the circle will be the centre of 
the gudgeon G; then the gears will be always right, al¬ 
though the elevator rises and falls to suit the ship or tide. 
The top of these circular rabbets ought to be so fixed, 
that the lower end of the elevator may hang near the 
wall. This may be regulated by fixing the centre of 
the gudgeon G. The length of these rabbets is regu¬ 
lated by the distance the vessel is to rise and fall, to al¬ 
low the elevator to swing clear of the vessel when light, 
at high water. The best way to make the circular rab¬ 
bets is, to dress two pieces of 2-inch plank for each rab¬ 
bet, of the right circle, and to pin them to the posts, at 
such a distance, leaving the rabbet between them. 

When the gate and elevator are completed, and tried 
together, the gate hung in its rabbets, and played up and 
down, then the elevator may be raised by the same power 
that is to raise and lower it, as described, Art. 94. 


ARTICLE 96. 

OF THE MEAL ELEVATOR. 

Little need be said of the manner of constructing the 
meal elevator, after what has been said in Art. 90, ex¬ 
cept giving the dimensions. Make the pulleys 3! inches 
thick, and 18 inches diameter. Give them no more than 
20 revolutions in a minute. Make the strap 31 inches 
wide, of good, pliant, white harness leather; make buck¬ 
ets either of wood or sheet iron, to hold about half a pint 
each; put one for every foot of the strap; make the cases 
tight, especially round the upper pulley, slanting much 
at°bottom, so that the meal which falls out of the buckets 
may be guided into the descending case. Let it lean a 
little, that it may discharge the better. The spout that 
conveys the meal from the elevator to the hopper-boy, 
should not have much more than 45 degrees descent, 



238 CONSTRUCTION OF MACHINES. [CHAP. XI. 

that the meal may run easily down, and not cause a 
dust; fix it so that the meal will spread thinly over its 
bottom in its descent, and it will cool the better. Cover 
the top of the spout half way down, and hang a thin, 
light cloth, at the end of this cover, to check all the 
dust that may rise, by the fall of the meal from the 
buckets. Remember to take a large cipher off the in¬ 
side of the board, where it fits to the undermost side of 
the shaft of the upper pulley: the meal will otherwise 
work out along the shaft. Make all tight, as directed, 
and it will effectually prevent waste. 

In letting meal into an elevator, it must be let in some 
distance above the centre of the pulley, that it may fall 
clear from the spout that conveys it in; otherwise, it will 
clog and choke. Fig. 4, Plate VI., is the double socket 
gudgeon of the lower pulley, to which the conveyer joins. 
Fig. 3, a b c d, is a top view of the case that the pulley 
runs in, which is constructed thus; a b is a strong plank, 
14 by 3 inches, stepped in the sill, dove-tailed and keyed 
in the meal-beam, and is called the main bearer. In 
this, at the determined height, are framed the gudgeon 
bearers a c b d, which are planks 15 by 11 inches, set 71 
inches apart, the pulley running between, and resting on 
them. The end piece c d, 7 inches wide and 2 thick, 
is set in the direction of the strap case, and extends 5 
inches above the top of the pulley; to this the bearers 
are nailed. On the top of the bearers, above the gud¬ 
geons, are set two other planks, 13 by 11 inches, rab¬ 
beted into the main bearer, and screwed fast to the end 
piece c d: these are 4 inches above the pulley. The bot¬ 
tom piece of this case slides in between the bearers, rest¬ 
ing on two cleets, so that it can be drawn out to empty 
the case, if it should ever, by any means, be overcharged 
with meal: this completes the case. In the gudgeon 
bearer, under the gudgeons, are mortises, made about 
12 by 2 inches, for the meal to pass from the conveyer 
into the elevator; the bottom board of the conveyer 
trough rests on the bearer in these mortises. The strap- 
case joins to the top of the pulley-case, but is not made 
fast, but the back board of the descending case is stepped 


239 


CHAP. XI.] CONSTRUCTION OF MACHINES. 

into the inside of the top of the end piece c d. The 
bottom of the ascending case is to be supported steadily 
to its place, and the board at the bottom must be ci¬ 
phered off at the inside, with long and large ciphers, 
making them, at the point, only I of an inch thick; 
this is to make the bottom of the case wide for the buck¬ 
ets to enter, if any of them should be a little askew; 
the pulley-case is wider than the strap-cases, to give 
room for the meal from the conveyer to fall into the 
buckets; and, in order to keep the passage open, there 
is a piece 3 inches wide, and II inches thick, put on 
each side of the pulley, to stand at right angles with 
each other, extending 31 inches at each end, past the 
pulley; these are ciphered off so as to clear the strap, 
and draw the meal under the buckets: they are called 
bangers. 


ARTICLE 97. 

OF THE MEAL CONVEYER. 

Fig. 3. Plate VI., is a conveyer joined to the pulley of 
the elevator. (See it described Art. 88.) Fig. 4 is the 
gudgeon that is put through the lower pulley, to which 
the conveyer is joined by a socket, as represented. Fig. 
5 is a view of the said socket and the band, as it ap¬ 
pears on the end of the shaft. The tenon of the gudgeon 
is square, that the socket may lit it every way alike. 
Make the shaft inches diameter, of eight equal sides, 
and put on the socket and the gudgeon; then, to lay it out 
for the flights, begin at the pulley, mark as near the end 
as possible, on the one side, and, turning the shaft 
the way it is to work, at the distance of inches to¬ 
wards the other end, set a flight on the next side, and 
thus go on to mark for a flight on every side, still ad¬ 
vancing li inches to the other end, which will form the 
dotted spiral line, which would drive the meal the wrong 
way; but the flights are to be set across the spiral line, 



240 CONSTRUCTION OF MACHINES. [CHAP. XI. 

at an angle of about 30 degrees, with a line square 
across the shaft, and then they will drive the meal the 
right way, the flights operating like ploughs. 

To make the flights, take good maple, or other smooth 
hard wood, saw it into six inch lengths, split it always 
from the sap to the heart; make pieces 2\ inches wide, 
and I of an inch thick; plane them smooth on one side, 
and make a pattern to describe them by, and make a 
tenon 2\ inches long, to suit a I inch auger. When 
they are perfectly dry, having the shaft bored, and the 
inclination of the flights marked by a scribe, drive them 
in, and cut them off 2i inches from the shaft; dress 
them with their foremost edge sharp, taking all off from 
the backside, leaving the face smooth and straight, to 
push forward the meal: make their ends nearly circular. 
If the conveyer be short, put in lifting flights, with their 
broadside foremost, half the number of the others, be¬ 
tween the spires of them; they cool the meal by lifting 
and letting it fall over the shaft. 

To make the trough for it to run in, take 3 boards, the 
bottom one 11, back 15, and front 13 inches. Fix the 
block for the gudgeon to run in at one end, and fill the 
corners of the cleets, to make the bottom nearly circular, 
that but little meal may lie in it; join it neatly to the 
pulley-case, resting the bottom on the bottom of the hole 
cut for the meal to enter, and the other end on a sup¬ 
porter that it can be moved and put to its place again 
with ease, without stopping the elevator. 

A meal elevator and conveyer thus made, of good ma¬ 
terials, will last 50 years with very little repair, and save 
an immense quantity of meal from waste. The top of 
the trough must be left open, to let the stream of the 
meal out; and a door about 4 feet long, may be made in 
the ascending case of the elevator to buckle the strap, 
&c. The strap of the elevator turns the conveyer, so 
that it can be easily stopped if any thing should be caught 
in it; it is dangerous to turn it by cogs. This machine 
is often applied to cool the meal without the hopper-boy, 
and to attend the bolting-hopper, by extending it to 
a great length, and conveying the meal immediately 


CHAP. XI.] CONSTRUCTION OF MACHINES. 241 

into the hopper, which answers very well; but where 
there is room a hopper-boy is preferable. 


ARTICLE 98. 

% 

OF A GRAIN CONVEYER. 

This machine has been constructed in a variety of 
ways; the following appears to be the best, namely: 
First, make a round shaft, 9 inches diameter; and then, 
to make the spire, take strong sheet-iron, make a pattern 
3 inches broad, and of the true arch of a circle; the di¬ 
ameter of which (being the inside of the pattern) is to be 
12 inches; this will give it room to stretch along a 9 inch 
shaft, so as to make a rapid spiral, that will advance 
about 21 inches along the shaft every revolution. By 
this pattern cut the sheet-iron into circular pieces, and 
join the ends together by riveting and lapping them, so 
as to let the grain run freely over the joints; when they 
are joined together they will form several circles, one 
above the other, slip it on the shaft, and stretch it along 
as far as you can, till it comes tight to the shaft, and fas¬ 
ten it to its place by pins; set in the shaft at the back side 
of the spire, and nail it to the pins: it will now form a 
beautiful spiral, with returns 21 inches apart, which dis¬ 
tance is too great; there should, therefore, be two or three 
of these spirals made, and wound into each other, and 
all put on together, because, if one be put on first, the 
others cannot be got on so well afterwards; if there be 
three, they will then be 7 inches apart, and will convey 
wheat very fast. If these spirals be punched full of 
holes like a grater, and the trough be lined with sheet- 
iron, punched full of small holes, it will become an ex¬ 
cellent rubber; will clean the wheat of the dust and 
down that adhere to it, and supersede the necessity of 
any other rubbing machine. 

The spirals may also be formed with either wooden or 
16 



242 


CONSTRUCTION OF MACHINES. [CHAP. XI. 

iron flights, set so near to each other in the spiral lines 
as to convey the wheat from one to another. 


AHTICLE 99. 

v r 

OF THE HOPPER-BOY. 

This machine, also, has appeared under various con¬ 
structions, the best of which is represented by fig. 12, 
Plate VII. (See the description Art. 88.) 

To make the flight-arms C D, take a piece of dry pop¬ 
lar or other soft scantling 14 feet long, 8 by 2 2 inches in 
the middle, 5 by 11 inches at the end, and straight at the 
bottom; on this strike the middle line a b, fig. 13. Con¬ 
sider which way it is to revolve, and cipher off the under 
side of the foremost edge from the middle line, leaving 
the edge I of an inch thick, as appears by the shaded part. 
Then, to lay out the flights, take the following 


RULE. 

Set your compasses at 41 inches distance, and, begin¬ 
ning with one foot in the centre c, step towards the end 
b, observing to lessen the distance one-sixteenth part of 
an inch every step; this will set the flights closer toge¬ 
ther at the end than at the centre. Then, to set the 
flights of one arm to track truly between those of the 
other, and to find their inclination, with one point in the 
centre c, sweep the dotted circles across every point in 
one arm; then, without altering the centre or distance, 
make the little dotted marks on the other arm, and be¬ 
tween them the circles are to be swept for the flights in 
it. To vary their inclination regularly, from the end 
to the centre, strike the dotted line c d half an inch from 
the centre c, and 21 inches from the middle line at d, 
and then with the compasses set to half an inch, set off 
the inclination from the dotted circles, on the line c d; 
the line c d then approaches the middle line, the in- 



243 


CHAP. XI.] CONSTRUCTION OF MACHINES. 

clination is greater near the centre than at the end, and 
varies regularly. Dove-tail the flights into the arm, ob¬ 
serving to put the side that is to drive the meal, to the 
line of inclination. The bottoms of them should not 
extend past the middle line, the ends being all rounded 
and dressed off at the back side, to make the point 
sharp, leaving the driving side quite straight, like the 
flight r. (See them complete in the end c a.) The 
sweepers should be 5 or 6 inches long, screwed on be¬ 
hind the flights, at the back side of the arms, one at 
each end of the arm, and one at the part that passes 
over the hopper: their use is described in Art. 88. 

The upright shaft should be 4 by 4 inches, and made 
round for about 4£ feet at the lower end, to pass lightly 
through the centre of the arm. To keep the arm steady, 
there is a stay iron 15 inches high, its legs £ by I inch, 
to stride 2 feet. The ring at the top should fit the shaft 
neatly, and be smooth and rounded inside that it may 
slide easily up and down; by this the arm hangs to the 
rope that passes over a pulley at the top of the shaft, 8 
inches diameter, with a deep groove for the rope or cord 
to run in. Make the leading arm 6 by 11 inches in the 
middle, 2 by 1 inches at the end, and 8 feet long. This 
arm must be braced to the cog-wheel above, to keep it 
from splitting the shaft by an extra stress. 

The weight of the balance w, must be so nearly equal 
to the weight of the arm, that when it is raised to the 
top it will descend quietly. 

In the bottom of the upright shaft is the step-gudgeon 
(fig. 15) which passes through the square plate 4 by 4 
inches, (fig. 14;) on this plate the arm rests, before the 
flights touch the floor. The ring on the lower end of the 
shaft is less than the shaft, that it may pass through the 
arm: this gudgeon comes out every time the shaft is 
taken out of the arm. 

If the machine is to attend but one bolting-hopper, it 
need not be above 12 or 13 feet long. Set the upright 
shaft close to the hopper, and the flights all gather as 
the end c b, fig. 13. But if it is to attend, for the grind¬ 
ing of two pairs of stones, and two hoppers, make it 15 
feet long, and set it between them a little to one side of 


244 


CONSTRUCTION OF MACHINES. [CHAP. XI. 

both, so that the two ends may not both be over the hop¬ 
pers at the same time, which would make it run unstea¬ 
dily; then the flights between the hoppers and the cen¬ 
tre must drive the meal outwards to the sweepers, at 
the end c a, fig. 13. 

If it be to attend two hoppers, and cannot be set be¬ 
tween them for want of room, then set the shaft near to 
one of them; make the flights so that they will all gather 
to the centre, and put sweepers over the outer hopper, 
which will be first supplied, and the surplus carried to 
the other. The machine will regulate itself to attend 
both, although one should feed three times as fast as the 
other. 

If it be to attend three hoppers, set the shaft near the 
middle one, and put sweepers to fill the other two, the 
surplus will come to the centre one, and it will regulate 
to feed all three; but should the centre hopper ever stand 
while the others are going, (of either of these last appli¬ 
cations,) the flights next the centre must be moveable, 
that they may be turned, and set to drive the meal out 
from the centre. Hopper-boys should be driven by a 
strap in some part of their movement, that they may 
easily stop if any thing catch in them; but many mill¬ 
wrights prefer cogs: they should not revolve more than 
4 times in a minute. 


ARTICLE 100. 

OF THE DRILL. 

(See the description, Art. 88.) The pulleys should 
not be less than 10 inches diameter for meal, and for 
wheat more. The case they run in is a deep, narrow 
trough, say 16 inches deep, and 4 wide; pulleys and straps 
3 inches. The rakes are little, square blocks of willow 
or poplar, or any soft wood, that will not split by driving 
the nails; they should all be of one size, that each may 
take an equal quantity; they are nailed to the strap with 
long, small nails, with broad heads, which are inside the 
strap; the meal should always be let into them above the 



245 


CHAP XI.] CONSTRUCTION OF MACHINES. 

centre of the pulley, or at the top of it, to prevent its 
choking, which it is apt to do, if let in low. The motion 
should be slow for meal, but may be more lively for 
wheat. 

Directions for using a hopper-boy. 

1. When the meal elevator is set in motion to elevate 
the meal, the hopper-boy must be set in motion also, to 
spread and cool it; and as soon as the circle is full, the 
bolts may be started; the grinding and bolting may like¬ 
wise be carried on regularly together; which is the best 
way of working. 

2. But if you do not choose to bolt as you grind, turn 
up the feeding-sweepers, and let the hopper-boy spread 
and cool the meal, and rise over it; and when you be¬ 
gin to bolt, turn them down again. 

3. If you choose to keep the warm meal separate from 
the cool, shovel about 18 inches of the outside of the cir¬ 
cle in towards the centre, and turn the end flights, to 
drive the meal outwards; it will then spread the warm 
meal outwards, and gather the cool meal into the bolt¬ 
ing hopper. As soon as the ring is full with warm meal, 
rake it out of the reach of the hopper-boy, and let it fill 
again. 

4. To mix tail-flour or bran, &c., with a quantity of 
meal that is under the hopper-boy, make a hole for it in 
the meal quite to the floor, and put it in; and the hop¬ 
per-boy will mix it regularly with the hole. 

5. If it do not keep the hopper full, turn the feeding 
sweeper a little lower, and throw a little meal on the 
top of the arm, to make it sink deeper into the meal. 
If the spreading sweepers discharge their loads too soon, 
and do not trail the meal all around the circle, turn 
them a little lower; if they do not discharge, but keep 
too full, raise them a little. 


246 UTILITY OF THESE IMPROVEMENTS. [CHAP. XI. 


ARTICLE 101. 

OF THE UTILITY OF THESE INVENTIONS AND IMPROVEMENTS. 

1. In order to dry the meal in the most rapid and effec¬ 
tual manner, it is evident that it should be spread as thinly 
as possible, and be kept in motion from the moment it 
leaves the stones until it be cold, that it may have a fair 
opportunity of discharging its moisture, which will be 
done more effectually at that time, than after it has grown 
cold in a heap, and has retained its moisture: this imme¬ 
diate drying does not allow time for insects to deposite 
their eggs, which, in time, breed the worms that are often 
found in the heart of barrels of Hour well packed; and, 
by the moisture being expelled more effectually, it will 
not be so apt to sour. The first great advantage, there¬ 
fore, is, that the meal is better prepared for bolting , for 
packing , and for keeping , in much less time than usual. 

2. They do the work to much greater perfection , by 
cleaning the grain and screenings more effectually, hoist¬ 
ing and bolting over great part of the flour, and grinding 
and bolting over the middlings, all at one operation, 
mixing those parts that are to be mixed, and separating 
such as are to be separated. 

3. They save much meal from being wasted y if they be 
well constructed, because there is no necessity for tramp¬ 
ling in it, which trails it wherever we walk, nor shovel¬ 
ling it about to raise a dust that flies away, &c. This 
article of saving will soon pay the cost of making the 
machinery, and of keeping it in repair afterwards. 

4. They afford more room than they take up , because 
the whole of the meal loft, that heretofore was little 
enough to cool the meal on, may be spared for other 
uses, excepting the circle described by the hopper-boy; 
and the wheat garners may be filled from one story to 
another, up to the crane-spout, above the collar-beams, 
so that a small part of the house will hold an unusual 
quantity of wheat, and it may be drawn from the bot¬ 
tom into the elevator, as wanted. 

5. They tend to despatch business , by finishing as they 


CIIAP. XI.] UTILITY OF THESE IMPROVEMENTS. 247 

• 

go; so that there is not as much time expended in grind¬ 
ing over middlings, which will not employ the power of 
the mill, nor in cleaning and grinding the screenings, 
they being cleaned every few days and mixed with the 
wheat, and as the labour is easier, the miller can keep 
the stones in better order, and more regularly and steadi¬ 
ly at work, especially in the night time, when they fre¬ 
quently stop for want of help whereas, one man would 
be sufficient to attend six pairs of stones, running (in 
one house) with well constructed machinery. 

6. They last a long time with bat little expense of repair, 
because their motions are slow and easy. 

7. They hoist the grain and meal with less poicer, and 
disturb the motion of the mill much less than the old way. 
because the descending strap balances the ascending one, 
so that there is no more power used than to hoist the 
grain or meal itself; whereas, in the old way, for every 
3 bushels of wheat, which fill a 4 bushel tub with meal, 
the tub has to be hoisted, the-weight of which is equal to 
a bushel of wheat; consequently, the power used is as 3 
for the elevator to 4 for the tubs, which is one-fourth less 
with elevators than tubs; besides, the weight of 4 bush¬ 
els of wheat, thrown at once on the wheel, always 
checks the motion; before the tub is up, the stone sinks 
a little, and the mill is put out of tune every tub-full, 
which makes a great difference in a year’s grinding; 
this is worthy of notice when water is scarce. 

8. They save a great expense of attendance. One-half 
of the hands that were formerly required are now suffi¬ 
cient, and their labour is easier. Formerly, one hand 
was required for every 10 barrels of flour that the mill 
made daily; now, one for every 20 barrels is sufficient. 
A mill that made 40 barrels a day, required four men 
and a boy; two men are now sufficient. 


248 


BILLS OF MATERIALS. 


[CIIAP. XII. 


CHAPTER XII. 

BILLS OF MATERIALS TO BE PROVIDED FOR BUILDING AND 
CONSTRUCTING THE MACHINERY. 

ARTICLE 102. 

For a Wheat Elevator 43 feet high , with a Strap 4 inches 

icicle. 

Three sides of good, firm, white harness leather. 

220 feet of inch pine, or other boards that are dry, of 
about 12£ inches width, for the cases; these are to be 
dressed as follows:— 

86 feet in length, 7 inches wide, for the top and bottom. 

86 feet in length, 5 inches wide, with the edges truly 
squared, for the side boards. 

A quantity of inch boards for the garners, as they may 
be wanted. 

Sheet-iron, or a good butt of willow wood, for the buckets. 

2000 tacks, 14 and 16 ounce size, the largest about half 
an inch long, for the buckets. 

3 lbs. of 8 penny, and 1 lb. of 10 penny nails, for the 
cases. 

2 dozens of large, wood-screws, (but nails will do,) for 
pulley cases. 

16 feet of two-inch plank, for pulleys. 

16 feet of ditto, for cog-wheels, and dry pine scantling, 
41 by 4 1, or 5 by 5 inches to give it motion. 

Smith's Bill of Iron. 

1 double gudgeon I inch, (such as fig. 6, Plate VI.,) 5 
inches between the shoulders, 31 inches between the 
holes, the necks, or gudgeon part, 3 inches. 

1 small gudgeon, of the common size, 1 inch thick. 

1 gudgeon an inch thick, (fig. 7,) neck 31, tang 10 inches, 
to be next the upper pulley. 


BILLS OF MATERIALS. 


249 


CHAP. XII.] 

2 small bands, 44 inches from the outsides. 

1 harness-buckle, 4 inches from the outsides, with 2 
tongues, of the form of fig. 12. 

Add whatever more may be wanting for the gears, that 
are for giving it motion. 

For a Meal Elevator 43 Feet high , Strap 31 Inches wide , 
and a Conveyer for two pairs of Stones. 

270 feet of dry pine, or other inch boards; most of them 
111 or 12 inches wide, of any length, that they may 
suit to be dressed for the case boards, as follows: 

86 feet in length, 61 inches wide, for tops and bottoms 
of the cases. 

86 feet in length, 41 inches wide, for the side boards, 
truly squared at the edges. 

The back board of the conveyer trough 15 inches, bot¬ 
tom do. 11 inches, and front 13 inches wide. 

Some 2 inch plank for the pulleys and cog-wheels. 

Scantling for conveyers 6 by 6 or 51 by 51 inches, of 
dry pine or yellow poplar, (prefer light wood;) pine 
for shafts, 41 by 41 or 5 by 5 inches. 

21 sides of good, pliant harness leather. 

1500 of 14 ounce tacks. 

A good, clean butt of willow for buckets, unless the 
pieces that are left, which are too small for the wheat- 
buckets, w r ill make the meal-buckets. 

4 lbs. of 8 penny, and 1 lb. of 10 penny nails. 

2 dozens of large wood-screws, (nails w r ill do,) for the 
pulley cases. 


Smith's Bill of Iron. 

1 double gudgeon, (such as fig. 4, Plate VI.,) 11 inches 
thick, 71 inches between the necks, 31 between the 
key-holes, the necks 11 inches long, and the tenons at 
each end of the same length, exactly square, that the 
socket may fit every way alike. 

2 sockets, one for each tenon, such as appears on the one 
end of fig. 4. The distance between the outside of 
the straps, with the nails in, must be 51 inches; fig. 
5 is an end view of it, and the band that drives over 


250 BILLS OF MATERIALS. [CHAP. XII. 

it at the end of the shaft, as they appear on the end 
of the conveyer. 

2 small 4 inch gudgeons for the other ends of the con¬ 
veyers. 

4 thin bands 5? inches from the outsides, for the con¬ 
veyers. 

1 gudgeon an inch thick, neck 31 inches, and tang 10 
inches, for the shaft in the upper pulley; but if a 
gudgeon be put through the pulley, let it be of the 
form of fig. 6, with a tenon and socket at one end. 
like fig. 4. 

1 harness-buckle, 31 inches from the outsides, with two 
tongues; such as fig. 12, Plate YI. 

Add whatever more small gudgeons and bands may be 
necessary for giving motion. 

For a Hopper-Boy. 

1 piece of dry, hard, clean, pine scantling, 41 by 41 
inches, and 10 feet long, for the upright shaft. 

1 piece of dry poplar, soft pine, or other soft, light wood, 
not subject to crack and split in working, 8 by 21 
inches, 15 or 16 feet long, for the flight arms. 

Some two inch plank for wheels, to give it motion, and 
scantling 41 by 41 inches, for the shafts. 

60 flights, 6 inches long, 3 inches wide, and 1 inch at 
one, and 1 at the other edge, thinner at the fore than 
hind end, that they may drive in tight like a dove-tail 
wedge. These may be made out of green, hard ma¬ 
ple, split from sap to heart, and set to dry. 

Half a common bed-cord, for a leading line and balance- 
rope. 


Smith’s Bill of Iron. 

1 stay-iron, C F E, Plate VII., fig. 12. The height from 
the top of the ring F, to the bottom of the feet C E, 
is 15 inches; distance of the points of the feet C E, 24 
inches; size of the legs 1 by I inch; size of the ring F, 
1 by 4 inch, round and smooth inside; 4 inches diame¬ 
ter, the inside corners rounded off, to keep it from 
cutting the shaft; there must be two little loops, or 


CIIAP. XII.] MILL FOR HULLING RICE, ETC. 251 

eyes, one in each quarter, that the balance rope may 
be hung to either. 

2 screws with thumb-nuts, (that are turned by the thumb 
and fingers,) i of an inch thick, and 3 inches long, 
for the feet of the stay-iron. 

2 do. for the end flights, 3i inches long, rounded 14 
inches next the head, and square 11 inches next the 
screw, the round part thickest. 

2 do. for the end sweepers, 6 i inches long, rounded 1 
inch next the head, i inch thick. 

2 do. for the hopper sweepers, 82 inches long, and 1 
inch thick, or long nails, with rivet heads, will answer 
the purpose. 

1 step-gudgeon, (fig. 15,) 2 2 inches long below the ring. 

and tang 9 inches, I inch thick. 

1 plate, 4 by 4, and £ inch thick, for the step-gudgeon 
to pass through, (fig. 14.) 

1 band for the step-gudgeon, of inches diameter; from 
the outside it has to pass through the stay-iron. 

1 gudgeon and band, for the top of the shaft, gudgeon 
I inch, band 4 inches diameter, measuring the out¬ 
side. 

The smith can, by the book, easily understand how 
to make these irons; and the reader may, from these 
bills of materials, make a rough estimate of the whole 
expense, which he will find trifling, compared with 
their utility. 


ARTICLE 103. 

A MILL FOR CLEANING ANI) HULLING RICE. 

Fig. 2, Plate X. The rice brought to the mill in 
boats, is to be emptied into the hopper 1 , out of which 
it is conveyed by the conveyer into the elevator at 2 , 
which elevates it into the garner 3, on the third floor ; 
thence it descends into the garner 4, which hangs over 
the stones 5, and supplies them regularly. The stones 
are to be dressed with a few deep furrows, with but lit- 



252 


MILL FOR HULLING RICE, ETC. [CHAP. XII. 

tie draught, and picked full of large holes; they must be 
set more than the length of the grain apart. The hoop 
should be lined inside with strong sheet-iron, and this, 
if punched full of holes, will be thereby improved. The 
grain is to be kept under the stone as long as necessary: 
this is effected by forcing it to rise some distance up the 
hoop, to be discharged through a hole, which is to be 
raised, or lowered, by a gate sliding in the bottom of it. 

The principle by which the grains are hulled, is that 
of rubbing them against one another between the stones 
with great force; by which means they hull one another 
without being much broken by the stones. As the grain 
passes through the stones 5, it should fall into a rolling- 
screen or shaking-sieve 6, made of wire, with such 
meshes as will let out all the sand and dust, which may, 
if convenient, run through the floor into the water; the 
rice, and most of the heavy chaff, should fall through into 
the conveyer, which will convey it into the elevator at 
2. The light chaff, &c., that does not pass through the 
sieve, will fall out at the tail, and, if useless, may also 
run into the water and float away. There may be a 
fan put on the spindle, above the trundle, to make a 
light blast, to blow out the chaff and dust, which should 
be conveyed out through the wall, and this fan may 
supersede the necessity of the shaking-sieve. The grain 
and heavy chaff are to be elevated into garner 7; thence 
they are to descend into garner 8, and pass through 
the stones 9, which are to be fixed and dressed in the 
same way as the others, but are to rub the grain 
harder. The outside of the chaff, from its sharpness, 
will cut off all the inside hull from the grain, and leave 
it perfectly clean: as it falls from these last stones, it 
passes through the wind of the fan 10, fixed on the 
spindle of the stones 9, which will blow out the chaff 
and dust, and they then drop into the room 21; the 
wind should escape through the wall. There is a re¬ 
gulating board that moves on a joint at 21, so as to take 
all the grain into the conveyer, which will convey it 
into the elevator at 11, which elevates it into the gar¬ 
ner 12, to pass through the rolling-screen 13; this should 
have meshes of three different sizes; first, to take out the 
dust, which falls into part 17, by itself; secondly, to pass 


253 


CHAP. XII.] MILL FOR HULLING RICE, ETC. 

the small rice into apartment 16; the whole grains then 
fall into garner 14, perfectly clean, and are drawn into 
barrels at 15. The fan 18 blows out the dust, and lodges 
it in the room 19, and the wind passes out at 20; the 
head rice falls at the tail of the screen, and runs into 
the hopper of the stones 5, to go through the whole 
operation again. Thus, the whole work is completely 
performed by the water, with the help of the machinery, 
taking it from the boat, and operating upon it until it 
be put into the barrel, without the least manual labour. 

Perhaps it may be advantageous to make a few fur¬ 
rows in the edge of the stone, slanting at an angle of 
about 30 degrees, with a perpendicular line; these fur¬ 
rows will throw up the grain next the stone, on the top 
of that in the hoop, which will change its position con¬ 
tinually; but this, probably, may not be found neces¬ 
sary. 











' 



































• . 











































' 













■fin rt tljB /nurtjf. 

0;i the Process of Manufacturing Grain into Flour , as prac¬ 
tised by the most skilful Millers in the United States. 


CHAPTER XIII. 

ARTICLE 104. 

THE PRINCIPLES OF GRINDING EXPLAINED, TOGETHER WITH SOME 
OBSERVATIONS ON LAYING OUT THE FURROWS IN THE STONES WITH 
A PROPER DRAUGHT. 

The end we have in view in grinding the grain, is, to 
reduce it to such a degree of fineness, as is found by ex¬ 
perience to fit it to make the best bread; and to put it in 
such a state, that the flour may be most effectually se¬ 
parated from the bran, or skin of the grain, by means of 
sifting or bolting. It has been proved by experience, 
that to grind grain fine with dull mill-stones, will not an¬ 
swer said purpose, because it kills or destroys that qua¬ 
lity of the grain which causes it to ferment and rise 
in the baking; it also makes the meal so clammy that it 
sticks to the cloth, and chokes up the meshes in bolting; 
hence it appears, that it should be made fine with as 
little pressure as possible; and it is evident that this 
cannot be done without sharp instruments. Let us sup¬ 
pose we undertake to operate on one single grain: it 
seems to accord with reason, that we should first cut it 
into several pieces, with a sharp instrument, to put it 
into a state suitable for being .passed between two planes, 
in order to its being reduced to one regular degree of 



256 


PRINCIPLES OF GRINDING. [CHAP. XIII. 

fineness. The planes should have on their faces a num¬ 
ber of little sharp edges, to scrape off the meal from the 
bran, and should be set at such a distance apart as to 
reduce the meal to the required fineness, and no finer; 
so that no part can escape unground. The same rules 
or principles will apply to any quantity that will serve 
for one grain. 

To prepare the stones for grinding to the greatest 
perfection, we may conclude, therefore, that their faces 
must be put into such order that they will first cut the 
grain into several pieces, and then pass it between them 
in such a manner, that none can escape without being 
ground to a certain degree of fineness, whilst, at the 
same time, it scrapes the meal off cleanly from the bran 
or skin. 

The best way that I have yet found to effect this, is 
(after the stones are faced with the staff, and pick,) to 
grind between them a few quarts of fine, sharp sand; this 
will face them to fit each other so exactly, that no meal 
can pass them without being ground; this is also the best 
way of sharpening all the little edges on the face, that 
are formed by the pores of the stone; instead of sand, wa¬ 
ter may be used, the stones then face each other; they 
will then scrape the meal off of the bran, without too 
much pressure being applied. But as the meal will not 
pass from the centre to the periphery or verge of the 
stones, with sufficient rapidity, without some assistance, 
there must be a number of furrows, to aid it in its 
egress; and these furrows must be set with such a 
draught that the meal will not pass too far along them 
at once, without passing over the land, or plane, lest it 
should get out unground. They should also be of suffi¬ 
cient depth to permit air enough to pass through the 
stones to carry out the heat generated by the friction of 
grinding; but if they have too much draught, they will 
not bear to be deep, or the meal will escape along them 
unground. These furrows ought to be made sharp at the 
feather-edge, which is the hinder edge of the furrow, 
and the foremost edge of the land; this serves the pur¬ 
pose of cutting down the grain; they should be more nu¬ 
merous near the centre, because there the office of the 


257 


CHAP. XIII.] PRINCIPLES OF GRINDING. 

stone is to cut the grain, and near the periphery the of¬ 
fice of the two planes is to reduce the flour to the re¬ 
quired fineness, and scrape the bran clean, which is ef¬ 
fected by the edges formed by the numerous little pores 
with which the burr-stone abounds. We must consider, 
however, that it is not best to have the stones too sharp 
near the eye, because they then cut the bran too fine. 
The stones incline to keep open near the eye, unless they 
be too close. If they be porous, (near the eye,) and will 
keep open without picking, they will remain a little dull, 
which will flatten the bran, without cutting it too much : 
but if they be soft next the eye, they w r ill keep too open, 
and that part of the stone will be nearly useless: they, 
therefore, should be very hard and porous. 

It is also necessary that the face of the stone be dressed 
in such a form, as to allow room for the grain, or meal, in 
every stage of its passage between the stones. In order 
to understand this, let us conceive the stream of wheat, 
entering the eye of the stone, to be about the thickness 
of a man’s finger, but instantly spreading every way 
over the whole face of the stone; this stream must, there¬ 
fore, get thinner, as it approaches the periphery, where 
it would be thinner than a fine hair, if it did not pass 
slower as it becomes finer, and if the stones were not 
kept apart by the bran; for this reason the stones must 
be so dressed, that they will not touch at the centre 
within about a 16th or 20th part of an inch, but get 
closer gradually, till within about 10 or 12 inches from 
the verge of the stone, proportioned to the diameter, 
and from that part out they must fit nicely together. 
This close part is called the flouring of the stone. The 
furrows should be deep near the centre, to admit wheat 
in its chopped state, and the air, which tends to keep 
the stones cool. 


17 


258 


DRAUGHT OF MILL-STONES. [CHAP. XIII. 


ARTICLE 105. 

OF THE DRAUGHT NECESSARY TO BE GIVEN TO THE FURROWS OF 

MILL-STONES. 

% 

From these principles and ideas, and the laws of cen¬ 
tral forces, explained at Art. 13,1 form my judgment of 
the proper draught of the furrows, and the manner of 
dress; points in which I find but few of the best millers 
to agree; some prefer one kind, and some another, which 
shows that this necessary part of the miller’s art is not 
yet well understood. In order to illustrate this matter, 
I have constructed fig. 3, Plate XI. A B represents the 
eight-quarter, C D the twelve quarter, and E A the cen¬ 
tral dress. Now, we observe that in the eight-quarter 
dress, the short furrows as F have about five times as 
much draught as the long ones, and cross one another like 
a pair of shears, opened so wide that they will drive all be¬ 
fore them, and cut nothing, and if these furrows be deep, 
they will drive out the meal as soon as it gets into them, 
and thereby make much coarse meal, such as middlings 
and ship-stuff, or carnel: the twelve-quarter dress appears 
to be better; but the short furrows at G have about four 
times as much draught as the long ones, the advantage of 
which I cannot perceive, because, if we have once found 
the draught that is right for one furrow, so as to cause 
the meal to pass through the stone in a proper time, it 
appears reasonable that the draught of every other fur¬ 
row should be equal to it. 

In the central dress E A, the furrows have all one 
draught, and if we could once determine exactly how 
much is necessary, I have no doubt we should find this 
to be the correct plan; and I apprehend that we shall find 
the best draught to be in a certain proportion to the size 
and velocity of the stone; because the centrifugal force 
that the circular motion of the stones gives the meal, has 
a tendency to move it outwards, and this force will be in 
inverse proportion to the diameter of the stones, their 
velocities being the same, by the fourth law of circular 


259 


CHAP. XIII.] DRAUGHT OF MILL-STONES. 

motion. E e is a furrow of the running-stone, and we 
may see by the figure that the furrows cross one ano¬ 
ther at the centre at a much greater angle than near the 
periphery, which I conceive to he right, because the 
centrifugal force is much less towards the centre than 
near the periphery. But we must also consider that the 
grain,whole or but little broken, requires less draught and 
centrifugal force to send it out, than it does when ground 
tine; which shows that we must not, in practice, follow 
the theory laid down in Art. 13, respecting the laws of 
circular motion and central forces; because the grain, as 
it is ground into meal, is less affected by the central force 
to drive it out; the angles, therefore, with which the 
furrows cross each other, must be greater near the verge 
or skirt of the stone, and less near its centre, than would 
be assigned by that theory; and what ought to be the 
amount of this variation is a question which practice has 
not yet determined. 

From the whole of my speculations on this difficult 
subject, added to observations on my own and others’ 
practice and experience, I propose the following rule for 
laying out a five foot mill-stone. (See Fig. 1, Plate 
XI.) 

1. Describe a circle with 3 inches, and another with 6 
inches radius, round the centre of the stone. 

2. Divide the 3 inch space between these two circles 
into 4 spaces, by 3 circles equi-distant; call these five 
circles draught circles. 

3. Divide the stone into 5 parts, by describing 4 circles 
equi-distant between the eye and the verge. 

4. Divide the circumference of the stone into 18 equal 
parts, called quarters. 

5. Then take a straight-edged rule, lay one end at one 
of the quarters at 6, at the verge of the stone, and the 
other end at the outside draught circle, 6 inches from 
the centre of the stone, and draw, a line for the furrow 
from the verge of the stone to the circle 5; then shift 
the rule from draught circle 6, to the draught circle 
5, and continue the furrow line towards the centre, 
from circle 5 to 4; then shift in the rule to draught 
circle 4, and continue to 3; shift to 3, and continue to 


260 


DRAUGHT OF HILL-STONES. [CHAP. XIII. 

2; shift to 2, and continue to 1, and the curve of the 
furrow is formed, as 1—6 in the figure. 

6. To this curve form a pattern, by which to lay out 
all the remainder. 

The furrows with this curve will cross each other 
with the following angles, shown, fig. 1: 

At circle 1, which is the eye 

of the stone, at 75 degrees angle, 

— 2 - - 45 - 


o 

O 

4 

5 

6 


35 

81 

27 

23 


These angles, as shown by the lines G r, H r, G s, H s, 
&c., &c., will, 1 think, do well in practice, will grind 
smooth, and make but little coarse meal, &c. 

Supposing the greatest draught circle to be 6 inches 
radius, then, by theory, the angles would have been, 


At circle 1 

_ 9 


o 

O 


5 

6 


138 degrees angle. 

69 - 

46 - 

35.5 - 

27.5 - 

23 - 


If the draught circle had been 5 inches radius, and the 
furrows straight, the angles would then have been at 


circle. 


degrees. 


1 about 180 


And 6 inches from centre, as shown by 1 
lines Gl, HI, * j 

2 

3 

4 

5 

6 

Here the angles near the centre are much too great 
to grind, and they will push the grain before them: to 
remedy this disadvantage, take the aforesaid rule, which 
forms the furrows, as shown at 6—7, fig. 1, which is 4 
of 18 qrs. H 8 represents a furrow of the runner, sliow- 


— 110 

— 60 

— 38 

— 29 

— 23 

— 18 












261 


CHAP. XIII.] DRAUGHT OF MILL-STONES. 

ing the angles where they cross those of the bed-stones, 
in every part. Here I have supposed the extremes of 
the draught of 6 inches for the verge, and 3 inches for 
the eye of the stone, to be right for a stone 5 feet dia¬ 
meter, revolving 100 times in a minute; but of this I 
am by no means certain. Yet by experience the ex¬ 
tremes may be ascertained for stones of all sizes, with 
different velocities; no kind of dress, of which I can con¬ 
ceive, appears to me likely to be brought to perfection 
excepting this, and it certainly appears, both by reason 
and by inspecting the figure, that it will grind the smooth¬ 
est of all the different kinds exhibited in the plate. 

The principle of grinding is partly that of shears, 
clipping; the planes of the face of the stones serving 
as guides to keep the grain in the edge of the shears, 
the furrows and pores forming the edges; if the shears 
cross one another, at too great an angle, they cannot 
cut; it follows, therefore, that all the strokes of the pick 
should be parallel to the furrows. 

To give two stones of different-diameters the same 
draught, we must make their draught circles in direct 
proportion to their diameters; then the furrows of the 
upper and lower stones of each size will cross each other 
with equal angles in all proportional distances, from 
their centres to their peripheries. But when we come 
to consider that the mean circles of all stones are to 
have nearly equal velocities, and that their centrifugal 
forces will be in inverse proportion to their diameters, 
we must perceive that small stones must have much less 
draught than large ones,*in proportion to their diame¬ 
ters. (See the proportion for determining the draught, 
Art. 13.) 

It is very necessary that the true draught of the fur¬ 
rows should be determined to suit the velocity of the 
stone, because the centrifugal force of the meal will vary, 
as the squares of the velocity of the stone, by the fifth law 
of circular motion. But the error of the draught may 
be corrected, in some measure, by the depth of the fur¬ 
rows. The less the draught, the deeper must be the 
furrow; and the greater the draught, the shallower the 
furrow, to prevent the meal from escaping unground; 


262 


OF FACING MILL-STONES. [CHAP. XIII. 

but if the furrows be too shallow, there will not a suffi¬ 
cient quantity of air pass through the stones to keep 
them cool. But in the central dress the furrows meet 
so near together, that they cut the stones too much 
away at the centre, unless they be made too narrow; 
I, therefore, prefer what is called the quarter dress, but 
divided into so many quarters that there will be little 
difference between the draught of the furrows; suppose 
18 quarters in a 5 feet stone, then each quarter takes 
up about 101 inches of the circumference of the stone, 
which suits for a division into about 4 furrows and 4 
lands, if the stone be close; but, if it be open, 2 or 3 
furrows to each quarter will be enough. This rule will 
give 4 feet 6 inch stones, 16; and 5 feet 6 inch stones, 
21; and 6 feet stones, 23 quarters. But the number 
of quarters is not very important; it is better, however, 
to have too many than too few. If the quarters be few, 
the disadvantage of the short furrows crossing at too 
great an angle, and throwing out the meal too coarse, 
may be remedied by making the land widest next the 
verge, thereby turning the furrows toward the centre, 
when they will have less draught, as in the quarter H I, 
fig. 3. 


ARTICLE 106. 

OF FACING MILL-STONES. 

The burr mill-stones are generally left in such face by 
the maker, that the miller need not spend much labour 
and time on them with picks before he may hang them, 
and grind them together with water or dry sand. After 
they have been ground together for a sufficient length 
of time, they must be taken up, and the red staff tried 
over their faces, 1 * and if it touch in circles, the project- 


* The red staff is made longer than the diameter of the stones, and three 
inches thick on the edge, which is made perfectly straight; on this is rubbed 
red clay, mixed with water, which shows the highest parts of the faces of the 
stones, when rubbed over them, by leaving the red on those high parts. 



263 


CHAP. XIII.] OF FACING MILL-STONES. 

ing parts should be well cracked with picks, and again 
ground with a small quantity of water or sand; after this, 
take them up, and try the staff on them: picking off' the 
red parts as before, and repeat this operation, until the 
staff will touch nearly alike all the way across, and until 
the stone comes to a face in every part, that the quality 
thereof may plainly appear; then, with a red or black 
line, proceed to lay out the furrows, in the manner de¬ 
termined upon, from the observations already laid down 
in the last article. After having a fair view of the face 
and quality of the stone, we can judge of the number of 
furrows most suitable, observing that where the stone is 
most open and porous, fewer furrows will be wanted; but 
where it is close and smooth, the furrows ought to be 
more numerous, and both they and the lands narrow, 
(about Is inch wide,) that they may form a greater 
number of edges, to perform the grinding. The fur¬ 
rows, at the back, should be made nearly the depth of the 
thickness of a grain of wheat, but sloped up to a feather 
edge, not deeper than the thickness of a finger nail;* 
this edge is to be made as sharp as possible, which can¬ 
not be done without a very sharp, hard pick. When 
the furrows are all made, try the red staff over them, and 
if it touch near the centre, the marks must be quite taken 
off about a foot next to it, but observing to crack lighter 
the farther from it, so that when the stones are laid to¬ 
gether, they will not touch at the centre, by about one- 
twentieth part of an inch, and close gradually, so as to 
touch and fit exactly, for about 10 or 12 inches from the 
verge. If the stones be now well hung, having the facing 
and furrowing neatly done, they will be found in the 


* For the form of the bottom of the furrow, see fig. 3, Plate XI. The curve 
line e b shows the bottom, b the feather edge, and e the back part. If the bot¬ 
tom has been made square at the back, as at e, the grain would lie in the cor¬ 
ner, and by the centrifugal force, would work out along the furrows without 
passing over the lands, and a part would escape unground. The back edge must 
be sloped for two reasons; 1st, that the meal may be pushed on to the leather 
edge; 2dly, that the furrow may grow narrower, as the faces of the stones wear 
away, to give liberty to sharpen the feather edge, without making the furrows 
too wide. Fig. 5 represents the face of two stones, working together, the run¬ 
ner moving from a to d. When the furrows are just over each other, as at a, 
there is room for a grain of wheat; when they move to the position of b, it is 
flattened, and at c, is clipped in two by the feather edges, and the lands or planes 
operate on it, as at d. 


264 OF HANGING MILL-STONES. [dlAP. XIII. 

most excellent order that they can possibly be put, for 
grinding wheat, because they are in good face, fitting 
so neatly together that the wheat cannot escape un¬ 
ground, and all the edges being perfectly sharp, so that 
the grain can be ground into Hour, with the least pres¬ 
sure possible. 


ARTICLE 107. 

OF HANGING MILL-STONES. 

If the stone have a balance-ryne, it is an easy matter 
to hang it, for we have only to set the spindle perpendi¬ 
cular to the face of the bed-stone; which is done by fas¬ 
tening a staff on the cock-head of the spindle, so that the 
end may reach to the edge of the stone, and be near the 
face. In this end we put a piece of elastic material, such 
as whalebone or quill, so as to touch the stone, that, on 
turning the trundle-head, the quill may move round the 
edge of the stone, and when it is made to touch alike all 
the way round, by altering the wedges of the bridge, the 
stone may be laid down, and it will be ready hung; * 

"But here we must observe whether the stone be of a true balance, as it hangs 
on the cock-head, and, if not, it must be truly balanced, by running lead into 
the lightest side. This ought to be carefully attended to by the maker, because 
the stone may be made to balance truly when at rest; yet, if every opposite 
part do not balance each other truly, the stone may be greatly out of balance 
when in motion; and this is the reason why the bush of some stones can be kept 
tight but a few hours, while others will keep so for several months, the spindles 
being good, and the stones balanced when at rest. The reason why a stone 
that is balanced at rest will sometimes not be balanced in motion, is, that if 
the upper part be heaviest on one side, and the lower part be heaviest on the 
other side of the centre, the stone may balance at rest, yet, when set in motion, 
the heaviest parts draw outwards most, by the centrifugal force, which will put 
the stone out of balance while in motion; and if the stone be not round, the 
parts farthest from the centre will have the greatest centrifugal force, because 
the centrifugal force is as the square of the distance from the centre. The neck 
of the spindle will wear next the longest side, and the bush get loose; and this 
argues in favour of a stiff ryne. The best method that I have seen for hanging 
stones with stiff horned rynes, is as follows: Fix a screw to each horn to regu¬ 
late by, which is done thus—after the horns are bedded, sink under each horn 
a strong burr, through which the screw is to pass from the neck of the stone, 
and fasten them in with lead; then, after the stone is laid down, put in the 
screws from the top of the stone, screwing them till the points bear tightly on 



265 


CHAP. XIII.] OF HANGING MILL-STONES. 

but if we have a stiff ryne, it will be much more diffi¬ 
cult, because we have not only to fix the spindle per¬ 
pendicular to the face of the bed-stone, but must set 
the face of the runner perpendicular to the spindle; and 
all this must be done with the greatest exactness, be¬ 
cause the ryne, being stiff, will not give way to suffer 
the runner to form itself to the bed-stone, as will the 
balance-ryne. 

The bed of the ryne being first carefully cleaned out, 
the ryne is put into it and tied, until the stone be laid 
down on the cock-head; then we find the part that hangs 
lowest, and, by putting the hand thereon, we press the 
stone down a little, turning it about at the same time, 
and observing whether the lowest part touches the bed¬ 
stone equally all the way round; if it do not, it is ad¬ 
justed by altering the wedges of the bridge-tree, until 
it touches equally, and then the spindle will stand per¬ 
pendicular to the face of the bed-stone. Then, to set 
the face of the runner perpendicular, or square, to the 
spindle, we remain in the same place, turning the stone, 
and pressing on it at every horn of the ryne, as it passes, 
and observing whether the runner will touch the bed¬ 
stone equally at every horn, which, if it do not, we 
strike with an iron bar on the horn, that bears the stone 
highest, which, by its jarring, will settle itself better 
into its bed, and thereby let the stone down a little in 
that part; but, if this be not sufficient, there must be 
paper put on the top of the horn that lets the stone too 
low; observing to mark the high horns, that when the 
stone is taken up, a little may be taken off the bed, and 
the ryne will soon become so neatly bedded, that the 
stone will hang very easily. But I have always found 
that every time the stone is taken up, the bridge is 
moved a little out of place; or, in other words, the 
spindle moved a little from its true, perpendicular posi¬ 
tion with respect to the face of the bed-stone, which is 
a great objection to the stiff horn ryne; for if the spindle 
be thrown but very little out of place, the stones cannot 

the horn: then proceed to hang the stone, which is very easily done by turning 
the screws. 


266 OF REGULATING T1IE FEED, ETC. [CHAP. XIII. 

conic together equally; whilst, with a balance-ryne, if 
it be considerably out of place, it will do but little or no 
injury in the grinding, because the running-stone has 
liberty to form itself to the bed-stone. 


ARTICLE 108. 

OF REGULATING THE FEED AND WATER IN GRINDING. 

The stone being well hung, proceed to grind, and 
when all things are ready, draw as much water as is 
judged to be sufficient; then observe the motion of the 
stone, by the noise of the damsel, and feel the meal; if 
it be too coarse, and the motion too slow, give less feed, 
and it will grind finer, and the motion will be quicker; 
if it yet grind too coarse, lower the stones; then, if the 
motion be too slow, draw a little more water; but if the 
meal feel to be too low ground, and the motion right, 
raise the stone a little, and give a little more feed. If 
the motion and feed be too great, and the meal be ground 
too low, shut off part of the water. But if the motion 
be too slow, and the feed be too small, draw more water. 

The miller must here remember, that there is a cer¬ 
tain portion of feed that the stones will bear and grind 
well, which will be in proportion to their size, velocity, 
and sharpness, and, if these be exceeded, there will be 
a loss, as the grinding will not then be well done. But 
no rule can be laid down, to ascertain the proper por¬ 
tion of feed, a knowledge depending upon that skill 
which is only to be attained by practice; as is also the 
art of judging of the right fineness. I will, however, 
lay down such rules and directions as may be of some 
assistance to the beginner. 



CHAP. XIII.] 


OF GOOD GRINDING. 


267 


ARTICLE 109. 

RULE FOR JUDGING OF GOOD GRINDING. 

Catch your hand full of meal as it falls from the stones 
and feel it lightly between your fingers and thumb; and 
if it feel smooth, and not oily or clammy, and will not 
stick much to the hand, it shows it to be fine enough, 
and the stones to be sharp. If there be no lumps to be 
felt larger than the rest, but all is of one fineness, it shows 
the stones to be well faced, and the furrows not to have 
too much draught, as none has escaped unground. 

If the meal feel very smooth and oily, and stick much 
to the hand, it shows it to be too low ground, hard 
pressed, and the stones dull. 

If it feel in part oily, and in part coarse and lumpy, and 
will stick much to the hand, it shows that the stones have 
too much feed; or that they are dull, and badly faced; 
or have some furrows that have too much draught, or 
are too deep, or perhaps too steep at the back edge, as 
part has escaped unground, and part is too much pressed 
and low. 

Catch your hand full, and holding your palm up, shut 
it briskly; if the greatest quantity of the meal liy out 
and escape between your fingers, it shows it to be in a 
fine and lively state, the stones sharp, the bran thin, and 
that it will bolt well: but the greater the quantity that 
stays in the hand, the more faulty is the flour. 

Catch a handful of meal in a sieve, and sift the meal 
clean out of the bran; then feel it, and if it be soft and 
springy, or elastic, and also feels thin, with but little 
sticking to the inside of the bran, and no pieces found 
much thicker than the rest, the stones are shown to be 
sharp, and the grinding well done.* 

* Instead of a sieve, you may take a shovel and hold the point near the stream 
of meal, and it will catch part of the bran, with but little meal mixed with it; 
which may be separated by tossing it from one hand to the other, wiping the 
hand at each toss. 


268 DRESSING, SHARPENING, ETC. [CHAP. XIII. 

But if it be broad and stiff, and the inside white, it is 
a sure sign that the stones are dull or over-fed. If you 
find some parts that are much thicker and harder than 
the rest, such as half or quarter grains, it shows that 
there are some furrows that have too much draught, or 
are too deep or steep at the back edge; else, that you 
are grinding with less feed than the depth of the fur¬ 
rows and velocity of the stone will bear. 


ARTICLE] 110. 

OF DRESSING AND SHARPENING THE STONES WHEN DULL. 

When the stones get dull they must be taken up, that 
they may be sharpened: to do this in the best manner, 
we must be provided with sharp, hard picks, with which 
the feather edges of the furrows are to be dressed as sharp 
as possible; which cannot be done with soft or dull picks. 
The bottoms of the furrows are likewise to be dressed, to 
keep them of the proper depth; but here the dull picks 
may be used.* The straight staff must now, also, be run 
over the face carefully, and if there be any parts harder 
or higher than the rest, the red will be left on them; 
they must be cracked lightly with many cracks, to make 
them wear as fast as the softer parts, in order to keep 
the face good. These cracks also form the edges that 
help to clean the bran; and the harder and closer the 
stone, the more numerous are they to be. They are to 
be made with a very sharp pick, parallel to the furrows; 
the damper the grain, the more the stone is to be cracked; 
and the drier and harder it is, the smoother must the 
face be. The hard, smooth places which glaze, may be 
made to wear more evenly by striking them, either with 

* To prevent the steel from striking your fingers, take a piece of leather about 
5 by 6 inches square; make a hole through the middle, and put the handle of the 
pick through it, keeping it between your hands and the pick, making a loop in 
the lower edge, through which put one of your fingers, to keep up the lower 
part from the stone. 



CHAP. XIII.] DEGREE OF FINENESS FOR FLOUR. 269 

a smooth, or rough-faced hammer, many light strokes, 
until a dust begins to appear, which frets the flinty 
part, and makes it softer and sharper. The stone will 
never be in the best order for cleaning the bran, with¬ 
out first grinding a little sand, to sharpen all the little 
edges formed by the pores of the stone; the same sand 
may be used several times. The stones may be sharp¬ 
ened without being taken up, or even stopped; to do 
this, take half a pint of sand, and hold the shoe from 
knocking, to let them run empty; then pour in the sand, 
and this will take the glaze oft 1 the face, and whet up 
the edges so that they will grind considerably better: 
this ought to be often done.* 

Some are in the practice of letting stones run for 
months without being dressed; but I am well convinced 
that those who dress them well twice a week, are fully 
paid for their trouble. 


ARTICLE 111. 

OF THE MOST PROPER DEGREE OF FINENESS FOR FLOUR. * 

As to the most proper degree of fineness for flour, 
millers differ in their opinion; but a great majority, and 
many of the most experienced, and of the best j udgment, 
agree in this, that if the flour be made very fine, it will 
be killed, (as it is termed,) so that it will not rise or 
ferment so well in baking; but I have heard many good 
millers give it as their opinion, that flour cannot be made 
too fine, if ground with sharp, clean stones, provided 
they be not suffered to rub against each other; and some 
of those millers do actually reduce almost all the meal 
they get out of the wheat into superfine flour, by which 
means they have but two kinds; namely, superfine flour 
and horse-feed; which is what is left after the flour is 
made, and is not fit to make even the coarsest kind of 
ship-bread. 

* Care should be taken to prevent the sand from getting mixed with the meal; 
it should be caught in some vessel, the stone being suffered to run quite empty; 
the small quantity that will remain in the stone will not injure the Hour. 




270 


OF GARLIC, ETC. 


[cnAP. XIV. 


To test the properties of the finest flour, I contrived 
to catch so much of the dust of that which was floating 
about in the mill, as made a large loaf of bread, which 
was raised with the same yeast, and baked in the same 
oven, with other loaves, that were made out of the 
most lively meal; the loaf made of the dust of the flour 
was equally light, and as good, if not better, than any 
of the others; it was more moist, and pleasant to the 
taste, though made of flour that, from its fineness, felt 
like oil. 

I conclude, therefore, that it is not the degree of fine¬ 
ness that destroys the life of the flour, but the degree 
of heat produced by the too great pressure applied in 
grinding; and that flour may be reduced to the greatest 
degree of fineness, without injuring the quality, pro¬ 
vided it be done with sharp, clean stones, and with lit¬ 
tle pressure. 


CHAPTER XIY. 

ARTICLE 112. 

OP GARLIC, WITH DIRECTIONS FOR GRINDING WHEAT MIXED THERE¬ 
WITH, AND FOR DRESSING THE STONES SUITABLE THERETO. 

In many parts of America there is a species of onion, 
called garlic, that grows spontaneously with the wheat. 
It bears a head resembling a seed onion, which contains 
a number of grains about the size of a grain of wheat, but 
somewhat lighter.* It is of a glutinous texture, and ad- 

* The complete separation of this garlic from the wheat, is so difficult, that 
it has hitherto baffled all our art. Those grains that are larger, and those that 
are smaller than the wheat, can be separated by screens; and those that are 
much lighter, may be blown out by fans; but those that are of the same size, 
and nearly of the same weight, cannot be separated without putting the wheat 
in water, where the wheat will sink and the garlic swim. But this method is 
too tedious for the miller to practise, except it be once a year, to clean up the 
headings, rather than lose the wheat that is mixed with the garlic, which can¬ 
not be otherwise sufficiently separated. Great care should be taken by the 



CHAP. XIV.] OF GARLIC, ETC. 271 

lieres to the stone in such a manner as apparently to 
blunt the edges, so that they will not grind to any degree 
of perfection. We are, therefore, obliged to take the 
runner up, and wash the glaze off with water, scrubbing 
the faces with stiff brushes, and drying up the water with 
cloths or sponges; this laborious operation must be re¬ 
peated twice, or perhaps four times, in 24 hours, if there 
be about ten grains of garlic in a handful of wheat. 

To put the stones in the best order to grind garlicky 
wheat, they must be cracked roughly all over the face, 
and dressed more open about the eye; they then break 
the grains of garlic less suddenly, giving the glutinous 
substance of the garlic more time to incorporate itself 
with the meal, and preventing its adherence to the stone. 
The rougher the face, the longer will the stones grind, 
because the more time will the garlic be in filling all the 
edges. 

The best method that I have ever yet discovered for 
manufacturing garlicky wheat is as follows, namely:— 

First, clean it over several times, in order to take out 
all the garlic that can be separated by the machinery, 
(which is easily done if you have a wheat elevator well 
fixed, as directed in Art. 94, Plate IX.,) then chop or 
half grind it, which will break the garlic, (it being softer 
than the wheat;) the moisture will then diffuse itself 
through the chopped wheat so that it will not injure the 
stones so much in the second grinding. By this means 
a considerable quantity can be ground, without taking 
up the stones. The chopping may be done at the rate 
of 15 or 20 bushels in an hour, and with but little trou¬ 
ble or loss of time, provided there be a meal elevator 
that will hoist it up to the meal loft, from whence it may 
descend to the hopper by spouts, to be ground a second 
time, when it will grind faster than if it had not been 
chopped. Great care should be taken, that it be not 
chopped so fine that it will not feed by the knocking of 
the shoe; as, likewise, that it be not too coarse, lest the 
garlic be not sufficiently broken. If the chopped grain 

farmers to prevent this troublesome thing from getting root in their farms; 
which, if it does, it will be almost impossible ever to root out again, as it pro¬ 
pagates both by seed and root, and is very hardy. 


272 OF GRINDING MIDDLINGS, ETC. [CHAP. XV. 

could lie a considerable time, the garlic would dry, and 
it would grind much better. 

But although every precaution be taken, if there be 
much garlic in the wheat, the bran will not be well 
cleaned; besides which there will be much coarse meal 
made, such as middlings and stuff, which will require to 
be ground over again, in order to make the most profit 
of the grain; this I shall treat of in the next chapter. 


CHAPTER XV. 

' ARTICLE 113. 

OF GRINDING THE MIDDLINGS OVER, AND, IF NECESSARY, THE STUFF 
AND BRAN, OR SHORTS, TO MAKE THE MOST OF THEM. 

Although we may grind the grain in the best manner 
we possibly can, so as to make any reasonable despatch, 
there yet will appear in the bolting a species of coarse 
meal, called middlings, and stuff, a quality between su¬ 
perfine and shorts, which will contain a portion of the 
best part of the grain; but in this state they will make 
very coarse bread, and consequently will command but 
a low price. For this reason, it is oftentimes profitable 
to the miller to grind and bolt them over again, and to 
make them into superfine Hour and fine middlings: this 
may easily be done by proper management. 

The middlings are generally hoisted by tubs, and laid 
in a convenient place on the floor in the meal loft, near 
the hopper-boy, until there is a large quantity ga¬ 
thered: when the first good opportunity offers, it is 
bolted over without any bran or shorts mixed with it, in 
order to take out all that is already fine enough to pass 
through the superfine cloth. The middlings will pass 
through the middlings’ cloth, and will then be round 
and lively, and in a state fit for grinding, being freed 



273 


CHAP. XV.] OF GRINDING MIDDLINGS. 

from the fine part that would have prevented it from 
feeding freely. The small specks of bran that were be¬ 
fore mixed with it, being lighter than the rich round 
part, will not pass through the middlings' cloth, but will 
pass on to the stuff’s cloth. The middlings will, by this 
means, be richer than before, and when made fine, may 
be mixed with the ground meal, and bolted into super¬ 
fine flour. 

The middlings may now be put into the hanging gar¬ 
ner over the hopper of the stones, out of which it will 
run into the hopper, and keep it full, as does the wheat, 
provided the garner be rightly constructed, and a hole 
about 6 by G inches made for it to issue out at. There 
must be a rod put through the bar, that supports the up¬ 
per end of the damsel, the lower end of which must reach 
into the eye of the stones, near to the bottom, and on one 
side thereof, to prevent the meal from sticking in the 
eye, which, if it does, it will not feed. The hole in the 
bottom of the hopper must not be less than four inches 
square. Things being thus prepared, and the stones be¬ 
ing sharp and clean, and nicely hung, draw a small quan¬ 
tity of water, (for meal does not require above one-tenth 
part that grain does,) taking great care to avoid pressure 
because the bran is not now between two stones, to pre¬ 
vent their coming too closely together. If you lay on as 
much weight as when grinding grain, the flour will be 
killed; but if the stones be well hung, and it be pressed 
lightly, the flour will be lively, and will make much bet¬ 
ter bread, without being bolted, than it would before it 
was ground. As fast as it is ground it may be elevated 
and bolted; but a little bran will now be necessary to 
keep the cloth open; and all that passes through the su¬ 
perfine cloth in this operation, may be mixed with what 
passed through in the first bolting of the middlings, and 
be hoisted up, and mixed (by the hopper-boy) regularly 
with the ground meal, and bolted into superfine flour, as 
directed Art. 89.* 

* All this trouble and loss of time may be saved by a little simple machinery, 
namely: as the middlings fall by the first bolting, let them be conveyed into 
the eye of the stone, and ground with the wheat as directed, Art. 81), plate VIII.; 
by which means, the whole thereof may be made into superfine flour, without 
any loss of time, or danger of being too hard pressed, for want of bran, to keep 

18 


274 


OF GRINDING MIDDLINGS. [CHAP. XV. 

The stuff, which is a degree coarser than middlings, it 
it be too poor for ship bread, and too rich to feed cattle 
on, is to be ground over in the same manner as the mid¬ 
dlings. But if it be mixed with fine flour, (as it some¬ 
times is,) so that it will not feed freely, it must be bolted 
over first: this will take out the fine flour, and also the 
fine specks of bran, which, being lightest, will come 
through the cloth last. When it is bolted the part that 
passes through the middlings’ and stuff’s parts of the 
cloth, are to be mixed and ground together; by this 
means the rich particles will be reduced to flour, and, 
when bolted, will pass through the finer cloths, and will 
make tolerably good bread. What passes through the 
middlings’ cloth will make but indifferent ship-bread, 
and what passes through the ship-stuff’s cloth will be 
what is called brown stuff, rougliings, or horse feed. 

The bran and shorts seldom are worth the trouble of 
grinding over, unless the stones have been very dull, or 
the grinding been but slightly performed, or the wheat 
very garlicky. When it is done the stones must be very 
sharp, and more water and pressure are required than in 
grinding grain. The flour, thus obtained, is generally of 
an indifferent quality, being made of that part of the 
grain that lies next the skin, and a great part of it is 
the skin itself, cut fine.* 


the stones apart. This mode I first introduced, and several others have since 
adopted it. 

* The merchant miller is to consider that there is a certain degree of close¬ 
ness or perfection that he is to aim at in manufacturing, which will yield him 
the greatest profit possible in a given time. And this degree of care and per¬ 
fection will vary with the prices of wheat and flour, so that what would yield 
the greatest profit at one time, would sink money at another; because, if the 
difference in the price of wheat and flour be but little, then we must make the 
irrain yield as much as possible, to obtain any profit. But if the price of flour 
be much above that of the wheat, then we had best make the greatest despatch, 
even if we should not do it so well, in order that the greater quantity may be 
done while these prices last: whereas, if we were to make such a despatch 
when the price of flour was but little above that of wheat, we should sink 
money. 


CHAP. XVI.] 


QUALITY OF MILL-STONES. ETC. 275 


CHAPTER XVI. 

ARTICLE 114. 

OF THE QUALITY OF MILL-STONES TO SUIT THE QUALITY OF THE 

WHEAT. 

It lias been found by experience that different quali¬ 
ties of wheat require different qualities of stones, to 
grind to the highest perfection. 

Although there be several species of wheat, of different 


A TABLE 

Showing the product of a bushel of wheat of different weights and, qua¬ 
lities, ascertained by experiments in grinding parcels. 


Weight per 
bushel. 

Superfine flour. 

Tail flour and 
middlings. 

Ship stuff. 

Bread stuff, 
shorts and bran. 

Screenings and 
loss in grinding. 

Proof. 

1 

* 

Quality of the grain.. 

! lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

' 59.5 

38.5 

3.68 

2.5 

13.1 

1.72 

59.5 

White wheat, clean. 

59. 

40.23 

3.65 

2.12 

12. 

1 . 

59. 

do 

do 

well cleaned. 

GO. 

38.7 

3.6 

1.61 

8.52 

7.57 

60. 

Red 

do 

not well cleaned. 

Gl. 

39.7 

5.68 

2.4 

9.54 

3.68 

61. 

White 

do 

mixed with green 










garlic. 

56. 

35.81 

5. 

1.85 

7.86 

5.48 

56. 

White 

do 

very clean. 

59.25 

35.26 

4.4 

1.47 

11.33 

6.79 

59.25 

Red 

do 

with some cockle 



I 







and light grains. 


If the screenings had been accurately weighed, and the loss in weight occa¬ 
sioned by the grinding ascertained, this table would have been more interesting. 
A loss of weight does take place by the evaporation of the moisture by the heat 
of the stones in the operation. 

The author conceived that if a complete separation of the skin of the wheat 
from the flour could be effected, and the flour be reduced to a sufficient degree of 
fineness, it might all pass for superfine; and having made the experiments in the 
table, he effected such improvements in the manufacture, by dressing the mill¬ 
stones to grind smooth; and by means of the machinery which he invented, re¬ 
turning the middlings into the eye of the stone, to be ground overwith the wheat, 
and elevating the tail-flour to the hopper-boy, to be bolted over again, &c., that 
in making his last 2000 barrels of superfine flour, he left no middlings or ship- 
stuff, which was not too poor for any kind of bread, excepting some small quan¬ 
tities which were retained in the mill; and the flour passed the inspection with 
credit. Others have since pursued the same principles, and put them more fully 
and completely into operation. 








































276 QUALITY OF MILL-STONES, ETC. [dlAP. XYI. 

qualities, yet, with respect to the grinding, we may 
divide them into three kinds only, namely:— 

1. The dry and hard. 

2. The damp and soft. 

3. Wheat that is mixed with garlic. 

When the grain that is to be ground is dry and hard, 
such as is raised on high and claj-ey lands, threshed in 
barns, and kept dry,* the stones for grinding it should 
be of that quality of the burr that is called close and 
hard, with few large pores, in order that they may have 
more face. The grain being brittle and easily broken 
into pieces, requires more face, or plane parts, (spoken 
of in Art. 104,) to reduce it to the required fineness, 
without cutting the skin too much. 

When the grain that is to be ground is somewhat damp 
and soft, such as is raised on a light sandy soil, is trodden 
out on the ground, and is carried in the holds of ships to 
market, which tends to increase the dampness, the stones 
should he more open and porous, because the grain is 
tough, difficult to be broken into pieces, and requires 
more sharp edges, and less face (or plane surface,) to re¬ 
duce it to the required fineness.-}- (See Art. 104.) 

When there is garlic or wild onion, (mentioned Art. 
Ill,) mixed with the wheat, the stones require to be 
open, porous and sharp; because the glutinous substance 
of the garlic adheres to the face of the stones, and blunts 
the edges; by which means little can be ground before 
the stones get so dull that they will require to be taken 
up and sharpened; and the more porous and sharp the 
stones are, the longer they will run, and grind a larger 
quantity without getting dull. There is a quality of the 
burr stone which may be denominated mellow or soft, 

* Such wheat as is produced by the mountains and clay lands of the country, 
distant from the'sea and tidewaters, is generally of a brownish colour, the grain 
appearing flinty, and sometimes the inside a little transparent, when cut by a 
sharp knife. This transparent kind of wheat is generally heavy, and of a thin 
skin, and will make as white flour, and as much of it, as the whitest grain. 

f Such is the wheat that is raised in all the low, level, and sandy lands of coun¬ 
tries near the sea and tide waters of America, where it is customary to tread out 
their wheat on the ground by horses, and where it sometimes gets wet by rain 
and dew, and the dampness of the ground. This grain is naturally of a fairer co¬ 
lour, and softer; and, when broken, the inside is white, which shov.C it to be 
nearer to a state of pulverization; it is more easily reduced to flour, and will 
not bear so much pressure as the grain that is raised on high and clay lands; or 
such that, when broken, appears solid and transparent. 


CHAP. XVII.] BOLTING REELS AND CLOTHS. 277 

to distinguish it from the kind which is hard and flinty: 
these are not so subject to glaze on the face; and it is 
found by experience that stones of this texture will grind 
at one dressing three or four times as much grain mixed 
with garlic, as those of a hard quality.* See Art. 111. 


CHAPTER XVII. 


ARTICLE 115. 

OF BOLTING REELS AND CLOTHS, WITH DIRECTIONS FOR BOLTING 

AND INSPECTING THE FLOUR. 

The effect we wish to produce by sifting, or bolting, 
is to separate the different qualities of flour from each 
other, and from the skin, shorts,or bran; let us nowin- 
quire which are the most proper means of attaining this 
end. 

t 

* It is very difficult to convey my ideas of the quality of the stones to the 
reader, for want of something with which to measure or compare their degrees 
of porosity or closeness, hardness or softness. The knowledge of these diffe¬ 
rent qualities is only to be attained by practice and experience; but I may ob¬ 
serve, that pores in the stone, larger in diameter than the length of a grain of 
wheat, are injurious; for how much soever they are larger, is so much loss of 
the face, because it is the edges that do the grinding; therefore all large pores 
in stones are a disadvantage. The greater the number of pores in the stones, 
so as to leave a sufficient quantity of touching surface, to reduce the flour to a 
sufficient degree of fineness, the better. 

Mill-stone makers ought to be acquainted W’ith the true principles on which 
grinding is performed, and with the art of manufacturing grain into flour, that 
they may be judges of the quality of the stones suitable to the quality of the 
wffieat of different parts of the country; also, of the best manner of disposing 
of the different pieces of stone, of different qualities, in the same mill-stone, ac¬ 
cording to the office of the several parts, from the centre to the verge of the stone. 
(See Art. 104.) 

Mill-stones are generally but very carelessly and slightly made; whereas, 
they should be made wfith the utmost care, and to the greatest nicety. The run¬ 
ner must be balanced exactly on its centre, and every corresponding opposite 
part of it should be of equal weight, or else the spindle will not keep tight in 
the bush; (see Art. 107;)—and if it is to be hung on a balance ryne, it should 
be put in at the formation of the stone, which should be nicely balanced thereon. 

But, above all, the kind of stone should be most attended to, that no piece of 
an unsuitable quality for the rest be put in; it being known to all experienced 
millers, that they had better give a high price for an extraordinarily good pair, 
than to have an indifferent pair for nothing. 



278 


BOLTING REELS AND CLOTHS. [CIIAP. XVII. 


Observations concerning Bolting. 

1. Suppose that we try a sieve, the meshes of which 
are so large as to let all the bran and meal through; it is 
evident that we could never thus attain the end pro¬ 
posed by the use thereof. 

2. Suppose we try a finer sieve, that will let all the 
meal through, but none of the bran; by this we cannot 
separate the different qualities of the Hour. 

o. We provide as many sieves of the different degrees 
of fineness as we intend to make different qualities of 
Hour; and which, for distinction, we name—Superfine, 
Middlings, and Camel. 

The superfine sieve we make of meshes, so fine as to 
let through the superfine flour, but none of the mid¬ 
dlings: the middlings’ sieve so fine as to let the mid¬ 
dlings pass through, but none of the carnel: the carnel 
sieve so fine as to let none of the shorts or bran pass 
through. 

Now it is evident, that if we would continue the ope¬ 
ration long enough, with each sieve, beginning with the 
superfine, we might effect a complete separation; but 
if we do not continue the operation a sufficient length 
of time, with each sieve, the separation will not be com¬ 
plete, for part of the superfine will be left, and will pass 
through with the middlings, and part of the middlings 
with the carnel, and a part of the carnel with the shorts; 
and this would be a laborious and tedious work, if per¬ 
formed by hand. 

Many inventions have been made to facilitate this bu¬ 
siness, amongst which the circular sieve, or bolting reel, 
is one of the foremost: this was, at first, turned and fed 
by hand; and afterwards it was so contrived as to be 
turned by water. But many have been the errors in the 
application of this machine, either from having the cloths 
too coarse, by which means the middlings and small 
pieces of bran passed through with the superfine flour, 
and part of the carnel with the middlings: or by having 
the cloths too short when they are fine enough, so that 
the operation could not be continued a sufficient time to 


279 


CHAP. XVII.] OF INSPECTING FLOUR. 

take all the superfine out before it reach the middlings’ 
cloth, and all the middlings before it reach the carnel 
cloth. 

The late improvements made on bolting seem to be 
principally as follows, namely: 

1. The using finer cloths—but they were found to 
clog or choke up, when put on small reels of 22 inches 
diameter. 

2. The enlarging the diameter of the reels to 27 i 
inches, which gives the meal greater distance to fall, and 
causes it to strike harder against the cloth, which keeps 
it open. 

3. The lengthening the cloths, that the operation may 
be continued a sufficient length of time. 

4. The bolting a much larger portion of the flour 
over again, than was done formerly. 

The meal, as it is ground, must be hoisted to the meal 
loft, where it should be spread thin, and often stirred, 
that it may cool and dry, to prepare it for bolting. Af¬ 
ter it is bolted, the tail flour, or that part of the super¬ 
fine that falls last, and which is too full of specks of bran 
to pass for superfine, is to be hoisted up again, and mixed 
with the ground meal, to be bolted over again. This 
hoisting, spreading, mixing, and attending the bolting 
hoppers, in merchant mills, creates a great deal of hard 
labour, if performed by hand; and is never completely 
done at last: but all this, and much more of the labour 
of mills, can now be accomplished by machinery, moved 
by water. (See Part III.) 

Of Inspecting Flour. 

The miller must attain a knowledge of the standard 
quality passable in the market: to examine it whilst 
bolting, hold a clean piece of board under the bolt, 
moving it from head to tail, so as to catch a proportional 
quantity all the way, as far as is taken for superfine; 
then smoothing it well by pressing an even surface on it, 
will make the specks and colour more plainly appear; 
if it be not good enough, turn a little more of the tail 
to be bolted over. 


280 


THE MILLER’S DUTY. 


[chap. XVIII. 

If the flour appear darker than was expected from 
the quality of the grain, it shows the grinding to be too 
high and the bolting too near; because the finer the 
Hour, the whiter its colour. 

This proceeding requires a good light; therefore, the 
best way is for the miller to observe to what degree of 
poorness he may reduce his tail hour, of middlings, so as 
to be safe; by which means he may judge with much 
more safety in the night. But the quality of the tail 
flour, middlings, &c., will greatly vary in different mills; 
for those that have the late improvements for bolting 
over the tail hour, grinding over the middlings, &c., can 
make nearly all into superfine; whereas, in those that 
have them not, the quality that remains next to super¬ 
fine is common or hue hour; then rich middlings, ship 
stuff, &c. Those who have experience will perceive the 
difference in the profits. If the flour feel soft, dead, and 
oily, yet is white, it shows the stones to have been dull, 
and too much pressure used. If it appears lively, yet 
dark-coloured, and too full of very fine specks, it shows 
the stones to have been rough and sharp, and that it 
was ground high and bolted too closely. 


CHAPTER XVIII. 

Directions for Iceeping the mill , and the business of it , in 

good order. 


ARTICLE 116. 

TIIE DUTY OF THE MILLER. 

Tiie mill is supposed to be completely finished for 
merchant work on the new plan; supplied w r ith a stock 
of grain, flour casks, nails, brushes, picks, shovels, scales, 
weights, &c., when the millers enter on their duty. 

If there be two of them capable of standing watch, or 
taking charge of the mill, the time is generally divided 



281 


CHAP. XVIII.] THE MILLER’S DUTY. 

as follows. In tlie day-time they both attend to business, 
but one of them has the chief direction. The night is 
divided into two watches, the first of which ends at one 
o’clock in the morning, when the master miller should 
enter on his watch, and continue till day-light, that he 
may be ready to direct other hands to their business 
early. The first thing he should do when his watch be¬ 
gins, is to see whether the stones are grinding, and the 
cloths bolting well. And, secondly, he should review 
all the moving gudgeons of the mill, to see whether any 
of them want grease, &c.: for want of this, the gudgeons 
often run dry and heat, which brings on heavy losses in 
time and repairs; for when they heat, they get a little 
loose, and the stones they run on crack, after which they 
cannot be kept cool. He should also see what quantity 
of grain is over the stones, and if there be not enough 
to supply them till morning, set the cleaning machines 
in motion. 

All things being set right, his duty is very easy—he 
has only to see to the machinery, the grinding and bolt¬ 
ing once in an hour; he has, therefore, plenty of time to 
amuse himself by reading, or otherwise. 

Early in the morning all the floors should be swept, 
and the flour dust collected; the casks nailed, weighed, 
marked, and branded, and the packing begun, that it 
may be completed in the fore part of the day; by this 
means, should any unforeseen thing occur, there will be 
spare time. Besides, to leave the packing till the after¬ 
noon, is a lazy practice, and keeps the business out of 
order. 

When the stones are to be sharpened, every tiling ne¬ 
cessary should be prepared before the mill is stopped, 
(especially if there be but one pair of stones to a water¬ 
wheel) that as little time as possible may be lost: the 
picks should be made quite sharp, and not be less than 
12 in number. Things being ready, the miller is then 
to take up the stones; set one hand to each, and dress 
them as soon as possible, that they may be set to work 
again; not forgetting to grease the gears and spindle 
foot. 

In the after part of the day a sufficient quantity of 


282 


ACCIDENTS BY FIRE. 


[CIIAP. XVIlx. 


grain is to be cleaned down, to supply the stones the 
whole night; because it is best to have nothing more to 
do in the night, than to attend to the grinding, bolting, 
gudgeons, &c. 


ARTICLE 117. 

PECULIAR ACCIDENTS BY WHICH MILLS ARE SUBJECT TO CATCH FIRE. 

1. There being many moving parts in a mill, if any 
piece of timber fall, and lie on any moving wheel, or 
shaft, and the velocity and pressure be great, it will ge¬ 
nerate fire, and perhaps consume the mill. 

2. Many people use wooden candlesticks, that may be 
set on a cask, bench, or the floor, and forgetting them, 
the candle burns down, sets the stick, cask, &c., on fire, 
which, perhaps, fnay not be discovered until the mill is 
in a flame. 

3. Careless millers sometimes stick a candle to a cask 
or post, and forget it until it has burnt a hole in the 
post, or set the cask on fire. 

4. Great quantities of grain sometimes bend the floor 
so as to press the head blocks against the top of the up¬ 
right shafts, and generate fire, (unless the head blocks 
have room to rise as the flour settles:) mill-wrights 
should consider this, and be careful to guard against it 
as they build. 

5. Branding irons carelessly laid down when hot, and 
left, might set a mill on fire. 

6. The foot of the mill-stone spindle, and gudgeons, 
frequently heat, and sometimes set the bridge-tree or 
shaft on fire. It is probable that, from such causes, 
mills have taken fire, when no person could discover 
how. 



CHAP. XVIII.] OF IMPROVING MILL-SEATS. 


283 


ARTICLE 118. 

OBSERVATIONS ON IMPROVING MILL SEATS. 

I may end this part with a few observations on im¬ 
proving mill-seats. The improvement of a mill-seat at 
a great expense, is an undertaking worthy of mature de¬ 
liberation, as wrong steps may increase it 10 per centum, 
and the improvement be incomplete; whereas, right 
steps may reduce it 10 per centum, and render them 
perfect. 

Strange as it may appear, it is yet a real fact that 
those who have least experience in the milling business 
frequently build the best and most complete mills. The 
reasons are evident— 

The professional man is bound to old systems, and re¬ 
lies on his own judgment in laying all his plans; where¬ 
as, the inexperienced man, being conscious of his defi¬ 
ciency, is perfectly free from all prejudice, and is disposed 
to call on all his experienced friends, and to collect all 
the improvements that are extant. 

A merchant who knows but little of the miller’s art, 
or of the structure or mechanism of mills, is naturally 
led to the following steps, namely:— 

He calls several of the most experienced millers and 
mill-wrights, to view the seat separately, and point out 
the spot for the mill-house, dam, &c., and notes their 
reasonings. The first, perhaps, fixes on a pretty level 
spot for the mill-house, and a certain rock, that nature 
seems to have prepared to support the breast of the dam, 
and an easy place to dig the race, mill-seat, &c. 

The second passes by these places without noticing 
them; explores the stream to the boundary line; fixes on 
another place, the only one he thinks appointed by na¬ 
ture for building a lasting dam—the foundation a solid 
rock, that cannot be undermined by the tumbling water; 
fixing on a rugged sjoot for the seat of the house; as- 
sisrninG: for his reasons, that the whole fall must be taken 
in, that all may be right at a future day. He is then 
informed of the opinion of the other, against which he 
gives substantial reasons. 



284 


OF IMPROVING MILL-SEATS. [CHAP. XVIII. 

The mill-wright, carpenter and mason, who are to un¬ 
dertake the building, are now called together to view the 
seat, fix on the spot for the house, dam, &c. After their 
opinions and reasons are heard, they are informed of the 
opinions and reasons of the others; all are joined toge¬ 
ther, and the places are fixed on. They are then desired 
to make out a complete draught of the plan for the house, 
&c., and to spare no pains; but to alter and improve on 
paper, till all appear to meet right, in the simplest and 
most convenient manner, (a week may be thus well 
spent,) making out complete bills of every piece of tim¬ 
ber, the quantity of boards, stone, lime, &c., a bill of iron¬ 
work, the number of wheels, their diameters, number of 
cogs, &c., &c., and every thing else required in the whole 
work. Each person can then make out his charge, and 
the costs can be very nearly counted. Every species of 
materials may be contracted for, to be delivered in due 
time: the work then goes on regularly without any dis¬ 
appointment; and when done, the improvements are 
complete, and a considerable sum of money is saved. 


tyul tljB jFiftjr. 


CHAPTER XIX. 

Practical Instructions for building Mills, ivithall their pro¬ 
portions, suitable to all falls, of from three to thirty-six 
feet. Received from Thomas Ellicott, Millwright. 


PREFATORY REMARKS. 

This part, as appears from the heading, was written 
by Mr. Thomas Ellicott; a part of his preface, published 
in the early editions of this work, it has been thought 
best to omit. After some remarks upon the defective 
operation of mills upon the old construction, he proceeds 
to say,— 

In the new way, all these inconveniences and disad¬ 
vantages are completely provided against: (See Plate 
XXII.,) which is a representation of the machinery, as 
applied in the whole process of the manufacture; taking 
the grain from the ship or wagon, and passing it through 
the whole process by water, until it is completely manu¬ 
factured into superfine flour. This is a mill of my plan¬ 
ning and draughting, now in actual practice, built on 
Occoquam river, in Virginia, with 3 water-wheels, and 
6 pairs of stones. 

If the wheat come by water to the mill, in the ship Z, 
it is measured and poured into the hopper A, and thence 
conveyed into the elevators at B, which elevates it, and 
drops it into the conveyer C D, which conveys it along 
under the joists of the second floor, and drops it into the 
hopper garner at D, out of which it is conveyed into the 





286 


TO THE READER. 


[CHAP. XIX. 

main wheat elevator at E, which carries it up in the 
peak of the roof, and delivers it into the rolling-screen 
at F, which (in this plan) is above the collar beams, out 
of which it falls into the hopper G, thence into the short 
elevator at H, which conveys it up into the fan I, from 
whence it runs down slanting, into the middle of the long 
conveyer at J, that runs towards both ends of the mill, 
and conveys the grain, as cleaned, into any garner 
K K K K K K, over all the stones, which is done by shift¬ 
ing a board under the fan, to guide the grain to either 
side of the cog-wheel J; and although each of these gar¬ 
ners should contain 2000 bushels of wheat over each pair 
of stones, 12000 bushels in 6 garners, yet nearly all may 
be ground out without handling it, and the feed of the 
stones will be more even and regular than is possible 
in the old way. As it is ground by the several pairs of 
stones, the meal falls into the conveyer at M M M, and 
is conveyed into the common meal elevator at N, which 
raises it to O; from thence it runs dowm the hopper-boy 
at P, which spreads and cools it over a circle of 10 or 
15 feet diameter, and (if thought best) will rise over it, 
and form a heap two or three feet high, perhaps thirty 
barrels of flour or more at a time, which may be bolted 
down at pleasure. When it is bolting, the hopper-boy 
gathers it into the bolting hoppers at Q, and attends them 
more regularly than is ever done by hand. As it is bolt¬ 
ed, the conveyer 11, in the bottom of the superfine chest, 
conveys the superfine flour to a hole through the floor 
at S, into the packing chest, which mixes it completely. 
Out of the packing chest it is fdled into the barrel at T, 
weighed in the scale U, packed at W by water, headed 
at X, and rolled to the door Y, then lowered down by a 
rope and windlass, into the ship again at Z. 

If the wheat come to the mill by land, in the wagon 
7, it is emptied from the bags into a spout that is in the 
wall, and it runs into the scale 8, which is large enough 
to hold a wagon load; and as it is weighed it is (by 
drawing a gate at bottom) let run into the garner D, 
out of which it is conveyed into the elevator at E, and 
so through the same process as before. 


TO THE READER. 


287 


CHAP. XIX.] 

As much of the tail of the superfine reels 37 as we 
think will not pass inspection, we suffer to pass on into 
the short elevator, (by shutting the gates at the bottom of 
the conveyer next the elevator, and opening one farther 
towards the other end.) The rubblings which fall at the 
tail of said reels are also hoisted into the bolting hoppers 
of the sifting reel 39, which is covered with a fine cloth, 
to take out all the fine flour dust, which will stick to the 
bran in warm damp weather; and all that passes through 
it is conveyed by the conveyer 40, into the elevator 41, 
which elevates it so high that it will run freely into the 
liopper-boy at 0, and is bolted over again with the 
ground meal. The rubblings that fall at the tail of the 
sifting-reel 39, fall into the hopper of the middlings’ reel 
42; and the bran falls at the tail into the lower story. 
Thus, you have it in your power, either by day or night, 
without any hand labour, except to shift the sliders, or 
some such trifle, to make your flour to suit the standard 
quality; and the greatest possible quantity of superfine 
is made out of the grain, and finished completely at one 
operation. 

Agreeably to request, I shall now attempt to show the 
method of making and putting water on the several 
kinds of water-wheels commonly used, with their di¬ 
mensions, &c., suited to falls and heads of from 3 to 36 
feet. I have also calculated tables for gearing them to 
mill-stones; and made draughts* of several water-wheels 
with their forebays, and manner of putting on the 
water, &c. 

Thomas Ellicott. 


* All my draughts are taken from a scale of eight feet to an inch, except Plat^ 
XVII., which is four feet to an inch. 


\ 



‘288 


OF UNDERSHOT MILLS. 


[CHAP. XIX. 


ARTICLE 119. 

OF UNDERSHOT MILLS. 

/ 

Fig. 1, Plate XIII., represents an undershot wheel 18 
feet diameter, with 3 feet total head and fall. It should 
be two feet wide for every foot the mill-stones are in di¬ 
ameter: that is, 8 feet between the shrouds for a 4 feet, 
andlO feet wide for a 5 feet stone. It should have three 
sets of arms and shrouds, on account of its great width. 
Its shaft should be at least 26 inches in diameter. It re¬ 
quires 12 arms 18 feet long, 31 inches thick, by 9 wide; 
and 24 shrouds, 71 feet long, 10 inches deep, by 3 thick, 
and 32 floats, 15 inches wide. Note.—It may he geared 
the same as an overshot wheel of equal diameter. Fig. 
2 represents the forebay, with its sills, posts, sluice and 
fail. I have, in this case, allowed 1 foot fall and 2 feet 
head. 

Fig. 3 represents an undershot wheel 18 feet diame¬ 
ter, with 7 feet head and hill. It should be as wide be¬ 
tween the shrouds as the stone is in diameter; its shaft 
should be 2 feet in diameter; requires 8 arms, 18 feet 
long, 31 inches thick, by 9 wide; and 16 shrouds, 71 feet 
long, 10 inches deep, by 3 thick. It may be geared the 
same as an overshot wheel 13 feet in diameter, because 
their revolutions per minute will be nearly equal. 

Fig. 4 represents the forebay, sluice and fall; the head 
and fall about equal. 

Fig. 5 represents an undershot wheel, 12 feet diame¬ 
ter, with 15 feet total head and fall. It should be 6 
inches wide for every foot the stone is in diameter. Its 
shaft 20 inches in diameter; requires 6 arms, 12 feet 
long, 3 by 8 inches; and 12 shrouds, 61 feet long, 21 
inches thick, and 8 deep. It suits well to be geared to 
a 5 feet stone with single gears, 60 cogs in the cog¬ 
wheel, and 16 rounds in the trundle; to a 41 feet stone, 
with 62 cogs and 15 rounds; and to a 4 feet stone with 
64 cogs and 14 rounds. These gears will do well till the 
fall is reduced to 12 feet, only the wheel must be less, as 


289 


CHAP. XIX.] OF UNDERSHOT MILLS. 

the falls are less so as to make the same number of revo¬ 
lutions in a minute; but this wheel requires more water 
than a breast-mill with the same fall. 

^ Fig. 6 is the forebay, gate, shute, and fall. Forebays 
should be wide, in proportion to the quantity of water 
they are to convey to the wheels, and should stand 8 
or 10 feet in the bank, and be firmly joined, to prevent 
the water from breaking through, which it will certainly 
do, unless they be well secured. 


ARTICLE 120. 

DIRECTIONS FOR MAKING FOREBAYS. 

The best way with which I am acquainted, for making 
this kind of forebays, is shown in Plate XVII., fig. 7. 
Make a number of solid frames, each consisting of a sill, 
two posts, and a cap; set them cross-wise, (as shown in 
the figure,) 21 or 3 feet apart; to these the planks are 
to be spiked, for there should be no sills lengthwise, as 
the water is apt to find its way along them. The frame 
at the head next the water, and one 6 or 8 feet down¬ 
wards in the bank, should extend 4 or 5 feet on each 
side of the forebay into the bank, and be planked in front, 
to prevent the water and vermin from working round. 
Both of the sills of these long frames should be well se¬ 
cured, by driving down plank, edge to edge, like piles, 
along the upper side, from end to end. 

The sills being settled on good foundations, the earth 
or gravel must be rammed well on all sides, full to the 
top of the sills. Then lay the bottom with good, sound 
plank, well jointed and spiked to the sills. Lay your 
shute, extending the upper end a little above the point 
of the gate when full drawn, to guide the water in a 
right direction to the wheel. Plank the head to its 
proper height, minding to leave a suitable sluice to guide 
the water smoothly down. Fix the gate in an upright 
position—hang the wheel, and finish it olf, ready for 
letting on the water. 

19 



290 


OF UNDERSHOT MILLS. 


[CHAP. XIX. 


A rack must be made across the stream, to keep oft* 
the floating matter that would break the floats and 
buckets of undershot, breast, and pitch-back wheels, and 
injure the gates. (See at the head of the forebay, fig. 7, 
Plate XVII.) This is done by setting a frame 3 feet in 
front of the forebay, and laying a sill 2 feet in front of 
it, for the bottom of the rack; in it the staves are put, 
made of laths, set edgewise with the stream, 2 inches 
apart, their upper ends nailed to the cap of the last frame; 
which causes them to lean down stream. The bottom of 
the race must be planked between the forebay and rack, 
to prevent the water from making a hole by tumbling 
through the rack when choked; and the sides must be 
planked outside of the post to keep up the banks. This 
rack must be twice as long as the forebay is wide, or 
else the water will not come fast enough through it to 
keep the head up; for the head is the spring of motion 
of an undershot mill. 


ARTICLE 121. 

ON THE PRINCIPLE OF UNDERSHOT MILLS. , 

They differ from all others in principle, because the 
water loses all its force by the first stroke against the 
floats; and the time this force is spending is.in propor¬ 
tion to the difference of the velocities of the wheel and 
the water, and the distance of the floats. Other mills 
have the weight of the water after the force of the head 
is spent, and will continue to move; but an undershot 
will stop as soon as the head is spent, as they depend 
not on the weight. They should be geared so that when 
the stone goes with a proper motion, the water-wheel 
will not run too fast, as they will not then receive the 
full force of the water; nor too slow, so as to lose its 
power by its rebounding and dashing over the buckets. 
This matter requires very close attention, and to find it 
out by theory, has puzzled our mechanical philosophers. 
They give us for a rule, that the wheel must move j ust one- 
third the velocity of the water: perhaps this may suit 



CHAP. XIX.] OF UNDERSHOT MILLS. 291 

where the head is not much higher than the float-hoards; 
but I am fully convined that it will not suit high heads. 

Experiments for determining the proper Motion for 

Undershot Wheels. 

I drew a full sluice of water on an undershot wheel 
with 15 feet head and fall, and counted its revolutions 
per minute; then geared it to a mill-stone, set it to work 
properly, and again counted its revolutions, and the dif¬ 
ference was not more than one-fourth slower. I believe, 
that if I had checked the motion of the wheel to be equal 
to one-third the motion of the water, the water would 
have rebounded and flown up to the shaft. Hence I 
conclude that the motion of the water must not be 
checked by the wheel more than one-third nor less than 
one-fourth, else it will lose in power; for although the 
wdieel will carry a greater load with a slow, than with a 
swift motion, yet it will not produce so great an effect, 
its motion being too slow. And again, if the motion be 
too swift, the load or resistance it will overcome will be 
so much less, that its effect will be lessened also. I con¬ 
clude that about two-thirds the velocity of the water is 
the proper motion for undershot wheels; the water will 
then spend all its force in the distance of two float-boards. 
It will be seen that I differ greatly with those learned 
authors who have concluded that the velocity of the 
wdieel ought to be but one-tliird of that of the water. To 
confute them, suppose the floats 12 inches, and the co¬ 
lumn of water striking them 8 inches deep: then, if two- 
thirds of the motion of this column be checked, it must 
instantly become 24 inches deep, and rebound against 
the backs of the floats, and the wdieel would be wallow¬ 
ing in this dead water; whereas, when only one-third of 
its motion is checked, it becomes 12 inches deep, and 
runs off from the wheel in a smooth and lively manner. 


292 


OF UNDERSHOT WHEELS. [CIIAF. XIX. 

Directions for gearing Undershot Wheels , 18 feet in diameter, 

where the head is above 3 and under 8 feet with double 

gears; counting the head from the point inhere the water 

strikes the floats. 

1. For 3 feet head and 18 feet wheel, see 18 feet wheel 
in the overshot table. 

2. For 3 feet 8 inches head, see 17 feet wheel in do. 

3. For 4 feet 4 inches head, see 16 feet wheel in do. 

4. For 5 feet head, see 15 feet wheel in do. 

5. For 5 feet 8 inches head, see 14 feet wheel in do. 

6. For 6 feet 4 inches head, see 13 feet wheel in do. 

7. For 7 feet head, see 12 feet wheel in do. 

The revolutions of the wheels will be nearly equal; 
therefore the gears may be the same. 

The following table is calculated to suit for any sized 
stone, from 4 to 6 feet diameter, different sized water¬ 
wheels from 12 to 18 feet diameter, and different heads 
from 8 to 20 feet above the point it strikes the floats; 
and to make 5 feet stones revolve 88 times; 4 feet 6 inch 
stones 97 times; and 4 feet stones 106 times in a mi¬ 
nute, when the water-wheel moves two-thirds the velo¬ 
city of the striking water. 

MILL-WRIGHTS’ table for undershot mills, single gear. 


Height of the head of 
water in feet. 

Diameter of the water¬ 
wheel in feet. 

Velocity of the wa¬ 
ter per minute in 
feet. 

Velocity of the water¬ 
wheel per minute in 
feet. 

Revolutions of the 
water wheel per mi¬ 
nute. 

Revolutions of the stone 
per minute. 

Number of cogs in the 
cog-wheel. 

Number of rounds in 
the trundle head. 

Revolutions of the mill¬ 
stone for one of the 
water wheels. 

Diameter of the stones 
in feet. 

8 

12 

1360 

906 

24 

88 

56 

15 

3| 

5 

9 

13 

1448 

965 

23£ 

88 

58 

15 

33 

5 

10 

14 

1521 

1014 

23 \ 

88 

58 

15 

3f 

5 

11 

15 

1595 

1061 

22| 

88 

58 

15 

3# 

5 

12 

16 

1666 

mi 

22i 

88 

58 

15 

3| 

5 

13 

16 

1735 

1157 

234 

88 

60 

16 

3§ 

5 

14 

16 

1800 

1200 

24 

88 

59 

16 

23 

5 

15 

16 

1863 

1242 

24f 

88 

60 

17 

33 

5 

16 

16 

1924 

1283 

251 

88 

59 

17 

3| 

5 

17 

17 

1983 

1322 

25 

88 

62 

17 

H 

5 

18 

17 

2041 

1361 

253 

88 

62 

17 

33 

5 

19 

18 

2097 

1398 

25 

88 

62 

17 

H 

5 

20 

18 

2152 

1435 

25§ 

88 

60 

17 

3§ 

5 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 























































CHAP. XX.] OF BREAST WHEELS. 293 

Note that there are nearly 60 cogs in the cog-wheel, 
in the foregoing table, and GO inches is the diameter of 
a 5 feet stone: therefore, it will do, without sensible er¬ 
ror, to put one cog more in the wheel for every inch 
that the stone is less than 60 inches diameter, down to 
4 feet; the trundle head and water-wheel remaining the 
same; and for every three inches that the stone is 
larger than 60 inches in diameter, put one round more 
in the trundle, and the motion of the stone will be 
nearly right up to 6 feet diameter. 


ARTICLE 122. 

OF BREAST WHEELS. 

Breast wheels differ but little in their structure or mo¬ 
tion, from overshot, excepting only that the water passes 
under instead of over them, and they must be wider in 
proportion as their fall is less. 

Fig. 1, Plate XIV., represents a low breast with 8 feet 
head and fall. It should be 9 inches wide for every 
foot of the diameter of the stone. Such wdieels are 
generally 18 feet diameter; the number and dimensions 
of their parts being as follows: 8 arms 18 feet long, 31 
by 9 inches; 16 shrouds 8 feet long, 21 by 9 inches; 56 
buckets; and shaft, 2 feet diameter. 

Fig. 2 shows the forebay, water-gate, and fall, and 
manner of striking on the water. 

Fig. 3 is a middling breast wheel, 18 feet diameter, 
with 12 feet head and fall. It should be 8 inches wide 
for every foot the stone is in diameter. 

Fig. 4 shows the forebay, gate, and fall, and manner 
of striking on the water. 

Figs. 5 and 6 is a high breast wheel, 16 feet diameter, 
witli 3 feet head in the forebay, and 10 feet fall. It 
should be 7 inches wide for every foot the stone is in dia¬ 
meter. The number and dimensions of its parts are 6 
arms, 16 feet long, 31 by 9 inches; 12 shrouds, 8 feet 
6 inches long, 21 by 8 or 9 inches deep, and 48 buckets. 



294 


OF PITCH-BACK WHEELS. [CHAP. XIX. 


ARTICLE 123. 

OF PITCII-BACK WHEELS. 

Pitch-back wheels are constructed exactly similar to 
breast wheels, only the water is struck on them at a 
greater height. Fig. 1, Plate XV"., is a wheel 18 feet dia¬ 
meter, with 3 feet head in the penstock, and 16 feet fall 
below it. It should be 6 inches wide for every foot of 
the diameter of the stone. 

Fig. 2 shows the trunk, penstock, gate, and fall; the 
gate sliding on the bottom of the penstock, and drawn by 
the lever A, turning on the roller. This wheel is much 
recommended by some mechanical philosophers, for the 
saving of water; but I do not join them in opinion, but 
think that an overshot with an equal head and fall, is 
fully equal to it in power; besides the saving of the ex¬ 
pense in building so high a wheel, and the greater diffi¬ 
culty of keeping it in order.* 


ARTICLE 124. 

OF OVERSHOT WHEELS. 

Overshot wheels receive their water'on the top, being 
moved by its weight: and are much to be recommended 
where there is fall enough for them. Fig. 3 represents 
one, 18 feet diameter, which should be about 6 inches 
wide for every foot the stone is in diameter. It should 
hang 8 or 9 inches clear of the tail-water, otherwise the 
water will be drawn back under it. The head in the 
penstock should be generally about 3 feet, which will 
spout the water about one-third faster than the wheel 
moves. Let the shute have about 3 inches fall, and di¬ 
rect the water into the wheel at the centre of its top. 

I have calculated a table for gearing overshot wheels, 
which will suit equally well any of the others of equal 
diameter, that have equal heads above the point where 
the water strikes the wheel. 


* On this subject see the Appendix. —Editor. 



295 


CHAP. XX.] OF OVERSHOT WHEELS. 

Dimensions of this wheel, 8 arms, 18 feet long, 3 by 
9 inches; 16 shrouds 7 feet 9 inches long, 21 by 7 or 8 
inches; 56 buckets, and shaft 24 inches diameter. 

Fig. 4 represents the penstock and trunk, &c., the wa¬ 
ter being let on the wheel by drawing the gate G. 

Fig. 1 and 2, Plate XVI., represents a low overshot, 
12 feet diameter, which should be in width equal to the 
diameter of the stone. Its parts and dimensions are, 6 
arms 12 feet long, 31 by 9 inches; 12 shrouds 61 feet 
long, 21 by 8 inches; shaft 22 inches diameter, and 30 
buckets. 

Fig. 3 represents a very high overshot, 30 feet diame¬ 
ter, which should be 31 inches wide for every foot of the 
diameter of the stone. Its parts and dimensions are, 6 
main arms, 30 feet long, 3i inches thick, 10 inches wide 
at the shaft, and 6 at the end; 12 short arms, 14 feet long, 
of equal dimensions; which are framed into the main 
arms near the shaft, as in the figure, for if they were all 
put through the shaft, they would make it too weak. 
The shaft should be 27 inches diameter, the whole being 
very heavy, and bearing a great load. Such high wheels 
require but little water. 


CHAPTER XX. 

ARTICLE 125. 

OF THE MOTION OF OVERSHOT WHEELS. 

After trying many experiments, I concluded that the 
circumference of overshot wheels geared to mill-stones, 
grinding to the best advantage, should move 550 feet in 
a minute; and that of the stones 1375 feet in the same 
time: that is, while the wheel moves 12, the stone moves 
30 inches, or in the proportion of 2 to 5. 

Then, to find how often the wheel we propose to make 
will revolve in a minute, take the following steps: 1st, 
Find the circumference of the wheel by multiplying the 
diameter by 22, and dividing by thus:— 



296 


OF GEARING. 


[CHAP. XX. 


Suppose the diameter to be 16 feet, 
then, 16 multiplied by 22, produces 352, 
which, divided by 7, gives 50 2-7 for the 
circumference. 

7)352 


22 


50 2-7 


By which we divide 550, the dis¬ 
tance the wheel moves in a minute, 
and it gives 11, for the revolutions of 
the wheel per minute, casting off the 
fraction 2-7, it being small. 


■\ 


> 


j 


510)5510 
11 times 


To find the revolutions of the stone 
per minute, 4 feet 6 inches (or 54 
inches) diameter, multiply 54 inches 
by 22, and divide by 7, and it gives 169 
5-7 (say 170) inches, the circumference 
of the stone. 



> 


j 


54 

22 


108 

108 


7)1188 


169 5-7 


By which divide 1375 feet, or 16500 
inches, the distance the skirt of the 
stone should move in a minute, and it 
gives 9 7; the revolutions of a stone per 
minute, 4J feet diameter. 


"N 


J 


1375 

12 


1710)165010(97 

153 


120 

119 


To find how often the stone revolves 
for once of the water-wheel, divide 97, 
the revolutions of the stone, by 11, the 
revolutions of the wheel, and it gives 8 
9-11, (say 9 times.) 




> 


i 


11)97 

8 9-11 


ARTICLE 126. 

OF GEARING. 

If the mill were to be single-geared, 99 cogs and 11 
rounds would give the stone the right motion, but the 
cog-wheel would then be too large and the trundle too 
small; it must, therefore, be double-geared. 




















297 


CHAP. XX.] OF GEARING. 

Suppose we choose 66 cogs in the big" 
cog-wheel, and 48 in the little one, and 
25 rounds in the wallower, and 15 in 
the trundle. 

Then to find the revolutions of the 
stone for one of the water-wheels, mul¬ 
tiply the cog-wheels together, and the 
wallower and trundle together, and di¬ 
vide one product by the other, and it 
will give the answer, 8]4|, not quite Si- 
revolutions, instead of 9. 

168 

We must, therefore, devise another proportion—Con¬ 
sidering which of the wheels we had best alter, and wish¬ 
ing not to alter the big cog-wheel or trundle, we put one 
round less in the wallower, and two cogs more in the 
little cog-wheel, and multiplying and dividing as before, 
we find the stone will turn 9 i times for once of the wa¬ 
ter-wheel, which is as near as we can get. The mill now 
stands thus, a 16 feet overshot wheel that will revolve 
11 times in a minute, geared to a stone 41 feet in diame¬ 
ter; the big cog-wheel 66 cogs, 41 inches from centre to 
centre of the cogs; (which we call the pitch of the gear) 
little cog-wheel 50 cogs, 41 pitch; wallower 24 rounds, 
41 pitch; and trundle 15 rounds, 41 inches pitch. 


15 


125 

25 


375 


66 

48 


528 

264 


375)3168(8 168-375 
3000 


ARTICLE 127. 


RULES FOR FINDING THE DIAMETER OF THE PITCH CIRCLES. 


To find the diameter of the pitch 
circle that the cogs stand in, multiply 
the number of cogs by the pitch, which 
gives the circumference; this multi¬ 
plied by 7, and divided by 22, gives the 
diameter in inches; which, divided by 
12, reduces it to feet and inches; thus: 


66 

4 


264 

33 


297 


22)2079(941 in. 
198 


99 

88 


11 

















298 FOR FINDING THE DIAMETER, ETC. [CHAP. XX. 

For the cog-wheel of 66 cogs, and 41 inches pitch, we 
find 7 feet 10 1 inches to be the diameter of the pitch 
circle; to which I add 8 inches for the outside ot the 
cogs, which makes 8 feet 61 inches, the diameter from 
out to out. 

By the same rules I find the diameters of the pitch 
circles of the other wheels to be as follows, namely:— 


feet. inches. 


Little cog-wheel 50 cogs, 41 1 g .. pitch cir 

inches pitch, J 

I add for the outside of the circle, 7 1 


Total diameter from out to out, 
Wallower 24 rounds, 41 inches | 
pitch, j 

Add, for outsides, 

Total diameter from the outsides, 
Trundle head 15 rounds, 41 } 

inches pitch, j 

Add, for outsides, 

Total diameter for the outsides, 


6 

o 

O 


2 

Hi 

do 

0 

Q 1 8 
"22 

do 

o 

o 


9 

O 


1 

81 2L 
^ * 2 2 

do 

0 

91 19 
-2 2 


1 

11 



Thus, we have completed the calculations for one mill, 
with a 16 feet overshot water-wheel, and stones 41 feet 
diameter. By the same rules we may calculate for 
wheels of all sizes from 12 to 30 feet, and stones from 4 
to 6 feet diameter, and may form tables that will be of 
great use even to master workmen, in despatching of bu¬ 
siness, in laying out work for their apprentices and other 
hands, in getting out timber, &c.; but more especially to 
those who are not sufficiently skilled in arithmetic to 
make the calculations. I have from long experience 
been sensible of the need of such tables, and have there¬ 
fore undertaken the task of preparing them. 





CHAP. XX.] EXPLANATION OF THE TABLES. 299 

ARTICLE 128. 

MILL-WEIGHTS’ TABLES, 

Calculated to suit overshot water-wheels with suita¬ 
ble heads above them, of all sizes, from 12 to 30 feet di¬ 
ameter, the velocity of their circumferences being about 
oo0 feet per minute, showing the number of cogs and 
rounds in all the wheels, double gear, to give the cir¬ 
cumference of the stone a velocity of 1375 feet per 
minute, also the diameter of their pitch circles, the di¬ 
ameter of the outsides, and revolutions of the water- 
wheel, and stones per minute. 

For particulars, see what is written over the head of 
each table. Table I. is to suit a 4 feet stone, Table II. 
a 4i, Table III. a 5 feet, and Table IV. a 51 feet stone. 

N. B. If the stones should be an inch or two larger or 
less than those above described, make use of the table 
that comes the nearest to it, and likewise for the water¬ 
wheels. For farther particulars see “ Draughting Mills.” 

Use of the following Tables. 

Having levelled your mill-seat, and found the total 
fall, after making due allowances for the fall in the races, 
and below the wheel, suppose there be 21 feet 9 inches, 
and the mill-stones be 4 feet in diameter, then look in 
Table I. (which is for 4 feet stones,) column 2, for the 
fall that is nearest yours, and you find it in the 7th 
example; and against it, in column 8, is 3 feet, the head 
proper to be above the wheel; in column 4 is 18 feet, 
for the diameter of the wheel, &c. for all the propor¬ 
tions of the gears to make a steady-moving mill; the 
stones to revolve 10G times in a minute.* 


* The following tables are calculated to give the stones the revolutions per 
minute mentioned in them, as near as any suitable number of cogs and rounds 
would permit, which motion I find is 8 or 10 revolutions per minute slower 
than proposed by Evans, in his table ;—his motion may do best in cases where 
there is plenty of power and steady work on one kind of grain ; but, in country 
mills, where they are continually changing from one kind to another, and often 
starting and stopping, I presume a slow motion will work most regularly. His 
table being calculated for only one size of mill-stones, and mine for four, any 
one choosing his motion, may look for the width of the water-wheel, number 
of cogs and rounds, size of the wheels to suit them, in the example following, 
keeping to my table in other respects, and you will have his motion nearly. 


300 


TABLES, ETC. 


[CHAP. XX. 


Table I. — For Overshot Mills, with stones 4 feet diameter, to 
revolve 106 times in a minute, pitch of the gear of the great 
cog-wheel and wallowers 4J inches, and of lesser cog-wheel 


and trundle 4J inches. 


No. of Examples. 

1 otai tails of water from the 

top of that in the penstock 

to that in the tail-race. 

Dillerent heads of water 

above the water-wheel. 

Luameters ol water-wheels 

from out to out. 

Widths of water-wheels in 

the clear. 

r\ • /* .-;-i 


ft. in. 

ft. in 

feet. 

ft. in 

1 

15 3 

2 6 

12 

3 0 

0 

/w 

16 4 

2 7 

13 

2 10 

3 

17 5 

2 8 

14 

2 8 ' 

4 

18 6 

2 9 

15 

2 6 

5 

19 7 

2 10 

16 

2 4 

6 

20 8 

2 11 

17 

2 3 

/ 

21 9 

3 0 

18 

2 2 

8 

22 10 

3 1 

19 

2 1 

9 

23 11 

3 2 

20 

2 0 

10 

25 1 

3 4 

21 

1 11 

11 

1 

26 3 

3 6 

22 

l 10 

12 

27 5 

3 8 

23 

1 9 ■ 

13 

28 7 

3 10 

24 

.8 j 

14 

29 9 

4 0 

25 

1 7 ! 

15 

30 11 

4 2 

26 

1 6 

( 

IG 

32 1 

4 4 

27 

> 5 :! 

17 

33 3 

4 6 

28 

■4 

>8 

34 6 

r 

4 9 

29 

13 ! 

19 

35 9 

5 0 ; 

30 

1 

- 1 


o 

5T £. 

Cfi O 
CD O 

aq 
o 02 
O E 
3q ^ 

k g 

cr cd 
CD aq 

CD -s 
ir- CD 

S° P 

r-f- 

P 

P 

CP 


j 66 
I 48 
j 69 
I 48 
[ 69 
I 48 
| 69 
t 50 
| 72 
» 52 
i 72 
1 52 
72 
52 
75 
52 
75 
52 
78 
52 
78 
52 
78 
54 
81 
54 
81 
56 
84 
56 
84 
58 
84 10 
56 6 
84 10 
56* 6 
87 10 
56 6 


7 
5 

8 
5 
8 
5 
8 
5 
8 
5 
8 
5 
8 
5 
8 
5 
8 
5 
9 
5 
9 

5 
9 

6 
9 
6 
9 
6 

10 

6 

10 

6 


Diameters of pitch circles of 
great and lesser wheels. 


Diameters of cog-wheels 
from out to out. 

No. of rounds in the wal¬ 
lowers and trundles. 


Diameters of pitch circles in 
wallowers and trundles. 


Total diameters of wallow¬ 
ers and trundles. 

lie volutions of great wheel 
per minute, nearly. 

t. in. 

ft. in. 


ft. in. 

ft. in. 


10. 5 

8 

6. 5 

25 

2 

11.75 

3 

3 

13 

4.87 

6 

0. 5 

15 

1 

8.33 

1 

11.33 

2.33 

8 

10.33 

25 

2 

11.73 

3 

3 

12.5 

4.87 

6 

0. 5 

15 

1 

8.33 

1 

11.33 

2.33 

8 

10.33 

26 

3 

1.25 

3 

5 25 

12 

4.87 

6 

0. 5 

15 

1 

8.33 

1 

11.33 

2.33 

8 

10.33 

25 

2 

11.75 

3 

3 

11.5 

7. 5 

6 

3 

15 

l 

8.33 

1 

11.33 

7.25 

9 

3 

26 

3 

1.25 

3 

5.25 

11 

10.33 

6 

6 

15 

1 

8.33 

l 

11.33 

7.25 

9 

3 

25 

2 

11.75 

3 

3 

10.5 

10.33 

6 

6 

14 

1 

7 

1 

10 

7-25 

9 

3 

24 

2 

10.33 

3 

1. 5 

10 

10.33 

6 

6 

14 

1 

7 

1 

10 

11.33 

9 

7.33 

24 

2 

10.33 

3 

1. 5 

9.66 

10.33 

6 

6 

14 

1 

7 

1 

10 

11.33 

9 

7.33 

23 

2 

9 

3 

0 

9.25 

10.33 

6 

6 

14 

1 

7 

l 

10 

3. 5 

9 

11. 5 

24 

2 

10.33 

3 

1. 5 

8.87 

10.33 

6 

6 

14 

1 

7 

1 

10 

3. 5 

9 

11. 5 

23 1 

2 

9 

3 

0 

8.5 

10.33 

6 

6 

H 

1 

'7 

1 

10 

3. 5 

9 

11. 5 

23 

2 

9 

3 

0 

8.25 

1 

6 

8. 5 

14 

1 

7 

1 

10 

8 

10 

4 

23 

2 

9 

3 

0 

8 

1 

6 

8. 5 

14 

1 

7 

1 

10 

8 

10 

4 

23 

2 

9 

3 

0 

7.75 

3.75 

6 

11.25 

14 

1 

7 

1 

10 

0.25 

10 

8.25 | 

23 

2 

9 

3 

0 


3.75 

6 

11.25 

14 

1 

7 

1 

10 

7.5 

0.25 

10 

8.25 

23 

2 

9 

3 

0 


6.25 

7 

1.75 

14 

1 

7 

1 

10 

6.75 

0.25 

10 

8.25 

23 

2 

9 

3 

0 

6.66 

3.75 

6 

11.25 

13 

1 

5.25 

1 

8.25 

0.25 

10 

8.25 

22 

2 

7. 5 

2 

10. 5 

6.5 

3.75 

6 

11.25 

13 

1 

5.25 

1 

8.25! 

5 

11 

1 

22 

2 

7. 5 

0 

10. 5 I 

6.25 

3.75 1 

6 

11.25 

13 

l 

6.25 

1 

8.251 
























































































CHAP. XX.] 


TABLES, ETC. 


301 


Table II.—For Overshot Mills, with stones 4 feet 6 inches di¬ 
ameter, to revolve 99 times in a minute, pitch of the gears 
4J and 4} inches. 

















































































302 


TABLES, ETC. 


[CIIAP. XX. 


Table III.—Stones 5 feet diameter, to revolve 86 times in a 
minute, the pitch of the gears 4J and 4J inches. 


No. of Examples. 

Total falls of water irom the 

top of that in the penstock 

to that in the tail-race. 


ft. in. 

1 

15 3 

2 

16 4 

3 

17 5 

4 

18 6 

5 

19 7 

6 

20 8 

7 

21 9 

8 

22 10 

9 

23 11 

10 

25 1 

11 

26 3 

12 

27 5 1 

13 

28 7 

14 

29 9 

15 

30 11 

16 

32 1 

17 

33 3 

18 

34 6 

19 

l 

35 9 


CO 




ft. in feet. 


0 


69 8 


6 


52 5 


2 3 


0 


56 6 
84 10 
56, 6 
84 10 
581 6 
84 10 
56 6 


Diameters of pitch circles of 

•L ...11 _ - _ _L 1 

Diameters of cog-wheels, 
from out to out. 

No. of rounds in the wal- 
lowers and trundles. 

Diameters of pitch circles 
in wallowers and trundles. 

I 

Total diameters of wallow¬ 
ers and trundles. 

in. 

ft. in. 


ft. in. 

ft. in. 

6.12 

8 

2.12 

26 

3 

1.25 ! 3 

4.25 

4 87 

6 

0. 5 

16 

1 

9.66 

2 

4.25 

10. 5 

8 

6. 5 

26 

3 

1.25 

3 

4.25 

4.87 

6 

0. 5 

16 

1 

9.66 

2 

4.25 

10. 5 

8 

6. 5 

25 

2 

11.75 

3 

3 

4.87 

6 

0. 5 

15 

1 

8.33 

1 

11.33 

2.33 

8 

10.33 

26 

3 

1.25 

3 

4.25 

4.87 

6 

0. 5 

15 

1 

8.33 

1 

11.33 

2 33 

8 

10.33 

25 

2 

11.75 

3 

3 

4.87 

6 

0. 5 

15 

1 

8.33 

1 

11. 5 

2.33 

8 

10.33 

25 

2 

11.75 

3 

3 

7. 5 

6 

3 

15 

1 

8.33 

1 

11. 5 

7.25 

9 

3 

26 

3 

1.25 

3 

4.25 

10.33 

6 

6 

15 

1 

8.33 

1 

11.33 

7.25 

9 

3 

25 

2 

11.75 3 

3 

10.33 

6 

6 

14 

1 

7 

1 

11. 5 

7.25 

9 

3 

24 

2 

10.33 

3 

2. 5 

10.33 

1 6 

6 

14 

1 

7 

1 

11. 5 

11.33 

9 

7.33 

24 

2 

10.33 

3 

2. 5 

10.33 

6 

6 

14 

1 

7 

1 

11. 5 

11.33 

! 9 

7.33 

23 

2 

9 

3 

0 

10.33 

6 

6 

14 

1 

7 

1 

11. 5 

3. 5 

1 9 

11. 5 

24 

2 

10.33 

3 

2.33 

10.33 

6 

6 

14 

1 

7 

1 

11. 5 

3. 5 

9 

11. 5 

23 

2 

9 

3 

0 

10.33 

6 

6 

14 

1 

7 

l 

11. 5 

3. 5 

9 

11. 5 

23 

2 

9 

3 

0 

1 

6 

8. 5 

14 

1 

7 

1 

11. 5 

8 

10 

4 

23 

2 

9 

3 

0 

1 

6 

8. 5 

14 

1 

7 

1 

11. 5 

8 

lo 

4 

23 

2 

9 

3 

0 

3.25 

6 

11.25 

14 

l 

7 

1 

11. 5 

0.25 

10 

8.25 

23 

2 

9 

3 

0 

3.25 

6 

11.25 

14 

1 

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/ 

1 

11. 5 

0.25 

10 

8.25 

23 

2 

9 

3 

0 

6.25 

1 7 

1.25 

14 

1 

7 

1 

11. 5 

0.25 

10 

8.25 

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9 

Q 

A* 

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1 6 

11.25 

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1 

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a 

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a c i 

r a 
a a J5 

cc ci 
p p 




ci 


13 

12.5 
12 

11.5 
11 

10.5 
10 

9.66 

9.25 
8.87 
8 

8.25 
8 


<+• r* 

/.75 


7.5 


6.66 


6.25 


6.25 














































































CHAP. XX.] TABLES, ETC. 


303 


Table IV. — For Overshot Mills, with stones 5 feet 6 inches di¬ 
ameter, to revolve 80 times in a minute, pitch of the gears 
4f and 4J inches. 


i\o. ol examples. 

1 olai tali 01 water Irom tlie 

top of that in the penstock 

to that in the tail-race. 

Inherent heads oi water 

above the water-wheels. 

Diameters ol water-wheels 

from out to out. 

1 

31 ^ 

1 Lt 

X 
«—*• 

Er 
o 0 

0 

pr 1 

CD p 

S’ CD 
P A 

—5 1 

* ^ 
to¬ 
co 

2L 

CO 

k—«• 

p 


ft. in. 

ft.in. 

feet 

ft.in. 

! 1 

i 15 3 

i 

2 6 

12 

4 6 

i 2 

16 4 

2 7 

13 

4 4 

1 3 

17 5 

2 8 

14 

4 2 

; 4 

18 6 

2 9 

15 

4 0 | 

! 5 

19 7 

2 10 

16 

3 10' 

6 

20 8 

2 11 

17 

3 8 j 

7 

21 9 

3 0 

18 

3 6 | 

8 

22 10 

3 1 

19 

3 4 

9 

23 11 

3 2 

20 

3 2 

10 

25 1 

3 4 

21 

3 0 

11 

26 3 

3 6 

22 

2 10 

12| 

27 5 

3 8 

23 

2 8 

13! 

28 7 

3 10 

24 

2 6 

14 i 

29 9 

4 0 

25 

2 4 

H 

30 11 

4 2 

26 

2 2 

16 

32 1 

4 4 

27 

2 0 

17 

33 3 

4 6 

28 

l 11 

18 

34 6 

4 9 

29 

1 10 

19 

35 9 

5 0 

30 

1 9 


2 

o 


CD »-t- 
cn n 

Cfl 2 
CD ® 

A 00. 
a * 
o j- 
Ciq P 


X CD 
CO crq 
CD -t 

S' p 

* r-h 

P 

P 

a. 


°s a 

g 5' 

h 3 

P CD 
Q S 

i—• CO 

CD 0 
co x, 

CO ^ 
CD T3 ' 

*2 S -' 
o Q 

O X 

°? o 

X o 

CD CD 
CD^ CO 

cS o 


O 
►—< • 

P 

3 

O CD 

3 S 

Is, 


c crc 

p d 


CD 

cT 


2 

c 


E c 

£•§ 
r-K C~^ 
2 CO 


X ^ 

s ^ 

C/J p 



ft. 

in. 

ft. 

in. 


ft. 

in. 

ft. 

in. 

60 

7 

6.75 

8 

2.75 

26 

3 

3.25 

3 

6.25 

48 

5 

8.75 

6 

4.25 

16 

1 

11 

2 

2 

63 

7 

11.12 

8 

7.12 

26 

3 

3.25 

3 

6.25 

48 

5 

8.75 

6 

4.25 

16 

1 

11 

2 

2 

66 

8 

3.75 

8 

11.75 

26 

3 

3.25 

3 

6.25 

48 

5 

8.75 

6 

4.25 

16 

1 

11 

2 

2 

66 

8 

3.75 

8 

11.75 

26 

3 

3.25 

3 

6.25 

48 

5 

8.75 

6 

4.25 

15 

1 

9. 5 

2 

0. 5 

69 

8 

8.33 

9 

4.33 

26 

3 

3.25 

3 

6.25 

48 

5 

8.75 

6 

4.25 

15 

1 

9. 5 

2 

0. 5 

69 

8 

8.33 

9 

4.33 

25 

3 

1.75 

3 

4 . 75 ! 

48 

5 

8.75 

6 

4.25 

15 

1 

9. 5 

2 

0. 5, 

69 

8 

8.33 

9 

4.33 

25 

3 

3.25 

3 

4.7 5 

50 

5 

11. 5 

6 

2. 5 

15 

1 

9. 5 

2 

0. 5 

72 

9 

0.75 

9 

8.75 

26 

3 

3.25 

3 

6.25 

52 

1 6 

2. 5 

6 

10 

14 

1 

8 

1 

11 

72 

9 

0.7 5 

9 

8.75 

25 

3 

1.75 

3 

4.75 

52 

6 

2. 5 

6 

10 

14 

1 

8 

l 

11 

72 

9 

0.75 

9 

8.75 

24 

3 

0.75 

3 

3.75 

52 

6 

2. 5 

6 

10 

14 

1 

8 

1 

11 

75 

9 

5.33 

10 

1.33 

24 

3 

0.75 

3 

3.75 

52 

6 

2. 5 

6 

10 

14 

1 

8 

1 

11 

75 

9 

5.33 

10 

1.33 

23 

2 

10.75 

3 

1.75 

52 

6 

2. 5 

6 

10 

14 

1 

8 

1 

11 

78 

9 

10. 5 

10 

6 

24 

3 

0.75 

3 

3.75 

52 

6 

2. 5 

6 

10 

14 

1 

8 

1 

11 

78 

9 

10. 5 

10 

6 

23 

2 

10.75 

3 

1.75 

52 

6 

2. 5 

6 

10 

14 

1 

8 

1 

11 

78 

9 

10. 5 

10 

6 

23 

2 

10.75 

3 

1.75 

54 

6 

5.33 

7 

1 

14 

1 

8 

l 

11 

81 

10 

2.‘ 5 

10 

10. 5 

23 

2 

10.75 

3 

1.75 

54 

6 

5.33 

7 

1 

14 

1 

8 

1 

11 

81 

10 

2. 5 

10 

10. 5 

23 

2 

10.75 

3 

1.75 1 

56 

6 

8 

7 

3. 5 

14 

1 

8 

1 

11 

84 

10 

7 

11 

3 

23 

2 

10.75 

3 

1.75 

56 

6 

8 

7 

3. 5 

14 

I 

8 

1 

11 

84 

10 

7 

11 

3 

23 

O 

10.75 

3 

1.75 

58 

6 

11 

7 

6. 5 

14 

1 

8 

1 

11 


5‘0 

23 513 

§ 3 

X CD 

sr r ~*~ 

O CD 

< CD 
CD 

5 ? 2 , 

^ o 
CT ^ 
3 o 


CD 

CO 


CD 

CO 


X 

o' 

p 

2 X 

CO £• 

.g 3 

X O 

r—■ 
r- O 

p CO 

P O 

X x, 

S 

CO 


I 05 

I CD 


CD 


EL 

o 


CO 

c 


CD X 

rc 


CD 


qc. 

o 


13 


1*3.5 


9.66 
' 9.25 

8.12 

8.5 

8.25 
8 

7.75 

7.5 I 
6.75; 

6.66 

6.5 

6.25 




























































































304 


OF CONSTRUCTING MILLS. [CHAP. XXL 


CHAPTER XXI. 

ARTICLE 129. 

DIRECTIONS FOR CONSTRUCTING UNDERSHOT WHEELS, SUCH AS SHOWN 

IN FIGURE 1, PLATE XIII. 

1. Dress the arms straight and square on all sides, and 
find the centre of each; divide each into 4 equal parts on 
the side, square, centre, scribe and gauge them from the 
upper side across each point, on both sides, 6 inches each 
way from the centre. 

2. Set up a truckle or centre post, for a centre to frame 
the wheel on, in a level piece of ground, and set a stake 
to keep up each end of the arms level with the truckle, 
of convenient height to work on. 

3. Lay the first arm with its centre on the centre of 
the truckle, and take a square notch out of the upper 
side 3-4ths of its depth, wide enough to receive the 2d 
arm. 

4. Make a square notch in the lower edge of the 2d 
arm, l-4th of its depth, and lay it in the other, and the}' 
will joint standing square across each other. 

5. Lay the 3d arm just equi-distant between the 
others, and scribe the lower arms by the side of the up¬ 
per, and the lower edge of the upper by the sides of the 
lower arms. Then take the upper arm off and strike 
the square scribes, taking out the lower half of the 3d 
arm, and the upper half of the lower arms, and fit and 
lay them together. 

6. Lay the fourth arm on the others, and scribe as di¬ 
rected before; then take 3-4ths of the lower edge of the 
4th arm, and 1-4th out of the upper edge of the others, 
and lay them together, and they will be locked together 
the depth of one. 

7. Make a sweep-staff with a gimlet hole for the cen¬ 
tre at one end, which must be set by a gimlet in the 
centre of the arms. Measure from this hole half the dia¬ 
meter of the wheel, making a hole there, and another the 
depth of the shrouds towards the centre, making each 
edge of this sweep at the end next the shrouds, straight 


CHAP. XXI.] OF CONSTRUCTING WHEELS . 305 

towards the centre hole, to scribe the ends of the shrouds 
by ' 

8. Circle both edges of the shrouds by the sweep, 
dress them to the proper width and thickness; lay out 
the laps 5 inches long; set a gauge to a little more than 
one-third their thickness; gauge all their ends for the 
laps from the outsides; cut them all out but the last, 
that it may be made a little longer, or shorter, as may 
suit to make the wheel the right diameter; sweep a circle 
on the arms to lay the shrouds to, while fitting them; 
put a small draw-pin in the middle of each lap, to draw 
the joints close; strike true circles both for the inside 
and outside of the shrouds, and 1 1 inch from the inside 
where the arms are to be let in. 

9. Divide the circle into 8 equal parts, coming as 
near the middle of each shroud as possible; strike a scribe 
across each to lay out the notch by, that is to be cut 1*1 
inch deep, to let in the arm at the bottom, where it is to 
be forked to take in the remainder of the shroud. Strike 
a scribe on the arms with the same sweep that the stroke 
for the notches on the shrouds was struck with. 

10. Scribe square down on each side of the arms, at 
the bottom, where they are to be forked; make a gauge 
to fit the arms; so wide as just to take in the shrouds, 
and leave 11 inch of wood outside of the mortise; bore 
1 or 2 holes through each end of the arms to draw-pin 
the shrouds to the arms when hung; mark all the arms 
and shrouds to their places, and take them apart. 

11. Fork the arms, put them together again, and put 
shrouds into the arms; draw-bore them, but not too 
much, which would be w r orse than too little; take the 
shrouds apart again, turn them the other side up, and 
draw r the joints together with the pins, and lay out the 
notches for 4 floats between each arm, 32 in all, large 
enough for admitting keys to keep them fast, but alloTv- 
ing them to drive in when any thing gets under the 
wheel. The ends of the floats must be dove-tailed a lit¬ 
tle into the shrouds; when one side is framed, frame the 
other to fellow it. This done, the -wheel is ready to 
hang, but remember to face the shrouds between the arms 

20 


306 


OF CONSTRUCTING WHEELS. [CHAP. XXI. 

with inch boards, nailed on with strong nails, to keep 
the wheel firmly together. 


ARTICLE 130. 

DIRECTIONS FOR DRESSING SHAFTS, &C. 

The shaft for a water wheel with 8 arms should be 
16 square, or 16 sided, about 2 feet diameter, the tree to 
make it being 2 feet 3 inches at the top end. When cut 
down, saw it off square at each end, and roll it on level 
skids, and if it be not straight, lay the rounding side 
down and view it, to find the spot for the centre at each 
end. Set the large compasses to half its diameter and 
sweep a circle at each end, plumb a line across each 
centre, and at each side of the circle, striking chalk lines 
over the plumb lines at each side from end to end, and 
dress off the sides plumb to these lines; turn it down on 
one side, setting it level; plumb line, and dress off the 
sides to a 4 square; set it exactly on one corner to 8 
square. In the same manner dress it to 16 square. 

To cut it square off to its exact length, stick a peg in 
the centre of each end, take a long square, (which may 
be made of boards,) lay it along the corner, the short 
end against the end of the peg, mark on the square 
where the shaft is to be cut, and mark the shaft by it 
at every corner line, from mark to mark; then cut it 
off to the lines, and it will be truly square. 


ARTICLE 131. 

TO LAY OUT THE MORTISES FOR TIIE ARMS. 

% 

Find the centre of the shaft at each end, and strike a 
circle; plumb a line through the centre at each end to 
be in the middle of two of the sides; make another scribe 
square across it; divide the distance equally between 
them, so as to divide the circle into 8 equal parts, and 




307 


CHAP. XXI.] OF CONSTRUCTING WHEELS. 

strike a line from each of them, from end to end, in the 
middle of the sides; measure from the top end about 3 
feet, and mark for the arm of the water-wheel, and the 
width of the wheel, and make another mark. Take a 
straight-edged 10 feet pole, and put the end even with 
the end of the shaft, and mark on it even with the marks 
on the shaft, and by these marks measure for the arm at 
every corner, marking and lining all the way round. 
Then take the uppermost arms of each rim, and by them 
lay out the mortises, about half an inch longer than they 
are wide, which is to leave key room; set the compasses 
a little more than half the thickness of the arms, and set 
one foot in the centre line at the end of the mortise, 
striking a scribe each way to lay out the width by; this 
done, lay out 2 more on the opposite side, to complete 
the mortises through the shaft. Lay out 2 more, square 
across the first, one-quarter the width of the arm longer, 
inwards, towards the middle of the wheel. Take notice 
which way the locks of the arms wind, whether to right 
or left, and lay out the third mortises to suit, else it will 
be a chance whether they suit or not: these must be half 
the width of the arms longer, inwards. 

The 4th set of mortises must be three-fourths longer 
inwards than the width of the arms; the mortises should 
be made rather hollowing than rounding, that the arms 
may slip in easily and stand fair. 

If there be 3 (which are called 6) arms to the cog¬ 
wheel, but one of them can be put through the sides of 
the shaft fairly; therefore, to lay out the mortises, divide 
the end of the shaft anew, into but 6 equal parts, by 
striking a circle on each end; and without altering the 
compasses, step from one of the old lines, six steps round 
the circle, and from these points strike chalk lines, and 
they will be the middle of the mortises, which may be 
laid out as before, minding which way the arms lock, and 
making two of the mortises one-third longer than the 
width of the arm, extending one on one side, and the 
other on the other side of the middle arm. 

If there be but 2 (called 4) arms in the cog-wheel, 
(which will do where the number of cogs does not exceed 
60) they will pass fairly through the sides, whether the 


308 


OF CONSTRUCTING WHEELS. [cnAP. XXI. 

shafts be 12 or 1G sided. One of these must be made 
one half longer than the width of the arms, to give room 
to put the arm in. 


ARTICLE 132. 

TO PUT IN THE GUDGEONS. 

Strike a circle on the ends of the shaft to let on the 
end bands; make a circle all round, 21 feet from each 
end, and saw a notch all round, half an inch deep. Lay 
out a square, round the centres, the size of the gudgeons, 
near the neck; lay the gudgeons straight on the shaft and 
scribe round them for their mortises; let them down with¬ 
in one-eighth of an inch of being in the centre. Dress 
off the ends to suit the bands; make 3 keys of good, sea¬ 
soned white oak, to fill each mortise above the gudgeons, 
to key them in, those next to the gudgeons to be 3i 
inches deep at the inner end, and 11 inch at their outer 
end, the v r edge or driving key 3 inches at the head, and 
6 inches longer than the mortise, that it may be cut off, 
if it batter in driving; the piece next the band so wide 
as to rise half an inch above the shaft, when all are laid 
in. Then take out all the keys and put on the bands, 
and make 8 or 12 iron wedges about 5 inches long by 2 
wide, l-3d inch thick, at the end, not much tapered ex¬ 
cept half an inch at the small end, on one side next the 
wood; by means of a set, drive them in on each side the 
gudgeon extremely hard, at a proper distance apart. 
Then put in the keys again, and lay a piece of iron un¬ 
der each band, between it and the key, 6 inches long, 
half an inch thick in the middle, and tapering off at the 
ends; then grease the keys well with tallow, and drive it 
well with a heavy sledge; after this, drive an iron wedge, 
half an inch from the two sides of each gudgeon, 5 inches 
long, about half an inch thick, and as wide as the gudgeon. 



CHAP. XXI.] OF CONSTRUCTING WHEELS. 


309 


ARTICLE 133. 

OF COG-WnEELS. 

The great face cog-wheels require 3 (called 6) arms, if 
the number of cogs exceed 54; if less, 4 will do. We 
find by the table, example 43, that the cog-wheel must 
have 69 cogs, with 44 inches pitch, the diameter of its 
pitch circle 8 feet 24 inches, and of its outsides 8 feet 104 
inches. It requires 3 arms, 9 feet long; 141 by 3 inches; 
12 cants, 64 feet long, 16 by 4 inches. (See it repre¬ 
sented, fig. 1, Plate XVII.) 

To frame it, dress and lock the arms together, (fig. 6, 
PI. XVII .) as directed, Art. 129, only mind to leave one- 
third of each arm uncut, and to lock them the right way 
to suit the winding of the mortises in the shaft, which is 
best found by putting a strip of board in the middle mor¬ 
tise, and supposing it to be the arm, mark which way it 
should be cut, then apply the board to the arm, and mark 
it. The arms being laid on a truckle, as directed, Art. 
129, make a sweep, the sides directing to the centre, 2 
feet from the outer end to scribe by; measure on the 
sweep, half the diameter of the wheel; and by it circle out 
the back edges of the cants, all of one width in the middle; 
dress them, keeping the best faces for the face side of 
the wheel; make a circle on the arms half an inch larger 
than the diameter of the wheel, laying three of the cants 
with their ends on the arms, at this circle, at equal dis¬ 
tances apart. Lay the other three on the top of them, 
so as to lap equally; scribe them both under and top, and 
gauge all for the laps from the face side; dress them out 
and lay them together, and joint them close; draw-pin 
them by an inch pin near their inside corners: this makes 
one-half of the wheel, shown fig. 5. Raise the centre 
level with that half; strike a circle near the outside, and 
find the centre of one of the cants: then, with the sweep 
that described the circle, step on the circle 6 steps, be¬ 
ginning at the middle of the cant, and these steps will 
show the middle of all the cants, or places for the arms. 
Make a scribe from the centre across each; strike another 
circle exactly at the corners, to place the corners of the 


310 


OF CONSTRUCTING WHEELS. [CHAP. XXI. 

next half by, and another about 2 1 inches farther out than 
the inside of the widest part of the cant, to let the arms 
in by; lay on three of the upper cants, the widest part 
over the narrowest part of the lower half, the inside to 
be at the point where the corner circle crosses the cen¬ 
tre lines. Saw off the ends, at the centre scribes, and fit 
them down to their places, doing the same with the rest. 
Lay them all on, and joint their ends together; draw-pin 
them to the lower half, by inch pins, 2 inches from their 
inner edges, and 9 inches from their ends. Raise the 
centre level with the wheel; plane a little of the rough 
off the face, and strike the pitch circle, and another 4 
inches inside, for the width of the face; strike another 
very near it, in which drive a chisel, half an inch deep, 
all round, and strike lines, with chalk, in the middle of 
the edge of the upper cants, and cut out of the solid, half 
of the upper cants, which raises the face; divide the 
pitch circle into 69 equal parts, 41 inches pitch, begin¬ 
ning and ending in a joint; strike two other circles each 
21 inches from the pitch circle, and strike central scribes 
between the cogs, and where they cross the circles put 
in pins, as many as there are cogs, half on each circle: 
find the lowest part on the face, and make the centre le¬ 
vel with it; look across in another place, square with the 
first and make it level with the centre also; then make the 
face straight, from these four places, and it will be true. 

Strike the pitch circle and divide it over again, and 
strike one circle on each side of it, 1 inch distance, for 
the cog mortises; sweep the outside of the wheel and in¬ 
side of the face, and two circles |ths of an inch from them 
to dress off the corners; strike a circle of two inches dia¬ 
meter on the centre of each cog, and with the sweep 
strike central scribes at each side of these circles for the 
cog mortises; bore and mortise half through; turn the 
wheel, dress and mortise the back side, leaving the arms 
from under it; strike a circle on the face edge of the 
arms, equal in diameter to that struck on the face of the 
half wheel, to let them in by; saw in square, and take 
out 41 inches, and let them into the back of the wheel 
11 inch deep, and bore a hole 11 inch into each arm, 
to pin it to the wheel. 


311 


CHAP. XXI.] SILLS, SPUR-BLOCKS, ETC. 

Strike a circle on the arms one inch less than the dia¬ 
meter of the shaft, make a key 8 inches long, lh thick, 
3i at the butt, and 2i inches at the top end, and by it lay 
out the mortises, two on each side of the shaft, in each 
arm to hang the wheel by. 


ARTICLE 134. 

OF SILLS, SPUR-BLOCKS AND HEAD-BLOCKS. 

See a side view of them in Plates XIII., XIV., XV., 
and XVI., and a top view of them, with their keys, at the 
end of the shaft, Plate XVIII. The sills are generally 
12 inches square. Lay them on the wall as firmly as 
possible, and one 3 feet farther out; on these lay the spurs, 
which are 5 feet long, 7 by 7 inches, 3 feet apart, notched 
and pinned to the sills: on these are set the head- 
blocks, 14 by 12 inches, 5 feet long, let down with a 
dove-tail shoulder between the spurs, to support keys 
to move it end-wise, and let two inches into the spurs 
with room for keys, to move it side-wise, and hold it to 
its place; see fig. 33 and 34, Plate XVIII. The ends 
of the shaft are let 2 inches into the head-blocks, to 
throw the weight more on the centre. 

Provide two stones, 5 or 6 inches square, very hard 
and clear of grit, for the gudgeons to run on, let them 
into the head-blocks, put the cog-wheel into its place, 
and then put in the shaft on the head-blocks, in its place. 

Put in the cog-wheel arm, lock them together, and pin 
the wheel to them; then hang the wheel, first by the 
keys to make it truly round, and then by side-wedges, 
to make it true in face; turn the wheel, and make two 
circles, one on each side of the cog-mortises, half an 
inch from them, so that the head of the cogs may stand 
between them equally. 


t 



312 


OF COGS. 


[chap. XXI. 


ARTICLE 135. 

OP COGS—THE BEST TIME FOR CUTTING AND MANNER OF SEASONING 

THEM. 

Cogs should be cut 14 inches long, and 31 inches 
square: this should be done when the sap runs at its 
fullest, at least a year before they are used, that they 
may dry without cracking. If either hickory or white 
oak be cut when the bark is set, they will worm-eat, 
and if dried hastily, will crack; to prevent which, boil 
them and dry them slowly, or soak them in water, a 
year, (20 years in mud and fresh water would not hurt 
them:) when they are taken out, they should be put in 
a liay-mow, under the hay, where, while foddered away, 
they will dry without cracking; but this often takes too 
long a time. I have discovered the following method 
of drying them in a few days, without cracking. I have 
a malt kiln with a floor of laths two inches apart; I 
shank the cogs, hang them shank downwards, between 
the laths, cover them with a hair cloth, make a wood 
fire, and the smoke prevents them from cracking. Some 
dry them in an oven, which ruins them. Boards, planks, 
or scantlings, are best dried in a kiln, covered so as to 
keep the smoke amongst them. Instead of a malt kiln, 
dig a cave in the side of a hill, 6 feet deep, 5 or 6 feet 
wide, with a post in each corner with plates on them, 
on which lay laths on edge, and pile the cogs on end, 
nearly perpendicular, so that the smoke can pass freely 
through or amongst them. Cover them slightly with 
boards and earth, make a slow fire, and close up the 
sides, and renew the fire once a day for 12 or 15 days; 
they will then dry without cracking. 


ARTICLE 136. 

OF SHANKING, TUTTING IN, AND DRESSING OFF COGS. 

Straighten one of the heart sides for the shank, make 
a pattern, the head 4, and shank 10 inches long, and 2 
inches wide at the head, II at the point; lay it on the 
cog, scribe the shank and shoulders, for the head, saw in 



CHAP. XXI.] OF COGS. ' 313 

and dress off the sides; make another pattern of the 
shank, without the head, to scribe the sides, and dress 
off the hacks by, laying it even with the face, which is 
to have no shoulder: take care, in dressing them off, 
that the axe do not strike the shoulder; if it do, it will 
crack there in drying, (if they be green;) lit and drive 
them in the mortises exceedingly tight, with their shoul¬ 
ders foremost, when at work. When the cogs are all in, 
fix two pieces of scantling, for rests, to scribe the cogs 
by, one across the cog-pit, near the cogs, another in front 
of them: fix them firmly. Hold a pointed tool on the 
rest, and scribe for the length of the cogs, by turning 
the wheel, and saw them off 3i inches long; then move 
the rest close to them, and fix it firmly; find the pitch 
circle on the end of the cogs, and, by turning the wheel, 
describe it there. 

Describe another line ith of an inch outside thereof, 
to set the compasses in to describe the face of the cogs 
by, and another at each side of the cogs to dress them to 
their width; then pitch the cogs by dividing them equal¬ 
ly, so that in stepping round, the compasses may end in 
the point where they began; describe a circle, in some 
particular place, with the pitch, that it may not be lost: 
these points must be as nearly as possible of a proper 
distance for the centre from the back of the cogs: find 
the cog to the back of which this point comes nearest, 
and set the compasses from that point to the back of 
the cog; with this distance set off the backs of all the 
cogs equally, on the circle, ith of an inch outside of the 
pitch circle, and from these points last made, set off the 
thickness of the cogs, which should, in this case, be li 
inch. 

Then describe the face and back of the cogs by setting 
the compasses in the hindmost point of one cog, and 
sweeping over the foremost point of another, for the 
face, and in the foremost point of one, sweeping over 
the hindmost of the other for the back part; dress them 
off on all sides, tapering about ith of an inch, in an inch 
distance; try them by a gauge, to make them all alike; 
take a little off the corners, and they are finished. 


314 of wAllowers and trundles, [ciiap. xxi. 


ARTICLE 1ST. 

OF THE LITTLE COG-WHEEL AND SHAFT. 

The process of making this is similar to that of the big 
cog-wheel. Its dimensions we find by the table, and the 
same example, (43,) to be 52 cogs, 44 pitch; diameter of 
pitch circle 5 feet 10 3 inches, and from out to out, 6 feet 
0 inches. 

It requires 2 arms, 6 feet 6 inches long, 11 by 34 
inches; 8 cants, 5 feet 6 inches, 17 by 34 inches. (See 
it Pig. 4, Plate XVII.) 

Of the Shaft. 

Dress it 8 feet long, 14 by 14 inches square, and de¬ 
scribe a circle on each end 14 inches diameter; strike 2 
lines through the centre, parallel to the sides, and divide 
the quarters into 4 equal parts, each; strike lines across 
the centre at each part at the end of these lines; strike 
chalk lines from end to end, to hew off the corners by, and 
it will be 8 square; lay out the mortises for the arms, put 
on the bands, and put in the gudgeons, as with the big 
shaft. 


ARTICLE 138. 

DIRECTIONS FOR MAKING WALLOWERS AND TRUNDLES. 

By example 43, in the table the wallower is to have 
26 rounds 44 pitch: the diameter of its pitch circle is 3 
feet 14 inch, and 3 feet 44 inches from outside: (see fig. 
3, plate XVII.) Its head should be 34 inches thick, dow¬ 
eled truly together, or made with double plank, crossing 
each other. Make the bands 3 inches wide, 4 th of an inch 
thick, evenly drawn; the heads must be made to suit the 
bands, by setting the compasses so that they will step 
round the inside of the band in 6 steps; with this distance 
sweep the head, allowing about T Lth of an inch outside, 
in dressing, to make such a large band tight. Make them 
hot alike all round with a chip fire, which swells the 
iron; put them on the head while hot, and cool them with 
water, to keep them from burning the wood too much, 



CHAP. XXI.] OF HANGING WHEELS. 315 

but not too fast, lest they snap: the same mode serves 
for hooping all kinds of heads. 

Dress the head fair after banding, and strike the pitch 
circle and divide it by the same pitch with the cogs; 
bore the holes for the rounds with an auger of at least 
11 inch; make the rounds of the best wood, 2| inches 
diameter, and 11 inches between the shoulders, the 
tenons 4 inches, to fit the holes loosely, until within 1 
inch of the shoulder, then drive it tight. Make the 
mortises for the shaft in the heads, with notches for the 
keys to hang it by. When the rounds are all driven 
into the shoulders, observe whether they stand straight; 
if not, they may be set fair by putting the wedges 
nearest to one side of the tenon, so that the strongest 
part may incline to draw them straight: this should be 
done with both heads. 


ARTICLE 139. 

OF FIXING THE nEAD-BLOCKS AND HANGING THE WHEELS. 

The head-blocks, for the wallower shaft are shown in 
Plate XVIII. Number 19 is one called a spur, G feet 
long and 15 inches deep, one end of which, at 19, is let 
1 inch into the top of the husk-sill, which sill is lh inch 
above the floor, the other end tenoned strongly into a 
strong post, 14 toy 14 inches 12 or 14 feet long, standing 
near the cog-wheel, on a sill in the bottom of the cog-pit; 
the top is tenoned into the husk-plank; these are called 
the tompkin posts. The other head-blocks appear at 20 
and 28. In these large head-blocks there are small ones 
let in that are 2 feet long, and 6 inches square, with a 
stone in each for the gudgeons to run on. That one in 
the spur 19 is made to slide, to put the wallower in and 
out of gear, by a lever screwed to its side. 

Lay the centre of the little shaft level with the big 
one, so as to put the wallower to gear -§ the thickness of 
the rounds deep, into the cog-wheel; put the shaft into 
its place, hang the wallower, and gauge the rounds to 
equal distance where the cogs take. Hang the cog-wheel, 



316 OF SINKING THE BALANCE-RYNE. [cnAP. XXI. 

put in the cogs, make the trundle as directed for the 
wallower. (See fig. 4, Plate XVII.) 


ARTICLE 140. 

DIRECTIONS FOR PUTTING IN THE BALANCE-RYNE. 

Lay it in the eye of the stone, and fix it truly in the 
centre; to do which, make a sweep by putting a long pin 
through the end, to reach into, and fit, the pivot hole in 
the balance-ryne; by repeated trials on the opposite side, 
fix it in the centre; then make a particular mark on the 
sweep, and others to suit it on the stone, scribe round 
the horns, and with picks and chisels sink the mortises 
to their proper depth, trying, by the particular marks 
made for the purpose, by the sweep, if it be in the centre. 
Put in the spindle with the foot upwards, and the driver 
on its place, while one holds it plumb. Set the driver 
over two of the horns, if it has four, but between them 
if it has but two. When the neck is exactly in the 
centre of the stone, scribe round the horns of the driver, 
and let into the stone, nearly to the balance, if it has 
four horns. Put the top of the spindle in the pivot-hole, 
to try whether the mortises let it down freely on both 
sides. 

Make a tram, to set the spindle square by, as follows: 
take a piece of board, cut a notch in one side, at one end, 
and hang it on the top of the spindle, by a little peg in 
the shoulder of the notch, to go into the hole in the foot, 
to keep it on: let the other end reach down to the edge 
of the stone; take another piece, circle out one end to fit 
the spindle neck, and make the other end fast to the low¬ 
er end of the hanging piece near the stone, so as to play 
round level with the face of the stone, resting on the 
centre-hole in the foot, and against the neck; put a bit 
of quill through the end of the level piece, that will touch 
the edge of the stone as it plays round. Make little 
wndges, and drive them in behind the horns of the driver, 
to keep both ends, at once, close to the sides of the mor¬ 
tises they bear against when at work, keeping the pivot 
or cock-head in its hole in the balance; try the tram gen- 



CHAP. XXI.] CRANE AND LIGHTER STAFF. 317 

tly round, and mark where the quill touches the stone 
first, and dress off the bearing sides of the mortises for the 
driver, until it will touch equally all round, giving the 
driver liberty to move endwise, and sidewise, so that the 
stone may rock an inch either way. The ryne and driver 
must be sunk |tlis of an inch below the face of the stone. 
Then hang the trundle firmly and truly on the spindle; 
put it in its place, to gear in the little cog-wheel. 


ARTICLE 141. 

TO BRIDGE THE SPINDLE. 

Make a little tram of a piece of lath, 3 inches wide at 
one end, and one inch at the other, make a mortise in the 
wide end, and put it on the cock-head, and a piece of 
quill in the small end, to play round the face of the stone; 
then, while one turns the trundle, another observes 
where the quill touches first, and alters the keys of the 
bridge-tree, driving the spindle-foot towards the part the 
quill touches, until it does so equally all round. Case 
the stone neatly round, within 2 inches of the face. 


ARTICLE 142. 

OE THE CRANE AND LIGHTER STAFF. 

Make a crane, with a screw and bale, for taking up 
and putting down the stone. (See it represented in 
Plate XI. fig 2 and 3.) Set the post out of the way as 
much as possible, let it be 9 by 6 inches in the middle, 
the arm 9 by 6, the brace 6 by 4; make a hole plumb 
over the spindle for the screw; put an iron washer on 
the arm under the female screw, nail it fast; the length of 
the screw in the worm part should exceed half the dia¬ 
meter of the stone, and it should reach 10 inches below 
it; the bale must touch only at the ends to give the stone 
liberty to turn, the pins to be 7 inches long, 1J thick, the 
bale to be 2 i inches wide in the middle, and II inches 
wide at the end; the whole should be made of the best 




318 


A HOOP FOR THE MILL-STONE. [CHAP. XXI. 

iron; for if either of them break, the danger would be 
great: the holes in the stones should be nearest to the up¬ 
per side of it. Raise the runner by the crane, screw, 
and bale, turn it and lay it down, with the horns of the 
driving ryne in their right places, as marked, it being 
down as it appears in Plate XXI., fig. 9. Make the 
lighter stalf C C, to raise and lower the stone in grinding, 
about 6 feet long, 31 by 21 inches at the large end, and 
2 inches square at the small end, with a knob on the up¬ 
per side. Make a mortise through the but-end, for the 
bray-iron to pass through, which goes into a mortise 4 
inches deep in the end of the bray at b, and is fastened 
with a pin; it may be 2 inches wide and half an inch 
thick made plain, with one hole at the lower, and 5 or 6 
at the upper end; it should be set in a staggering posi¬ 
tion. This lighter is fixed in front of the meal-beam, at 
such a height as to be handy to raise and lower at plea¬ 
sure; a weight of 41bs. is hung to the end of it by a strap, 
which laps two or three times round, and the other end 
is fastened to the post below, that keeps it in its place. 
Play the lighter up and down, and observe whether the 
stone rises and falls flat on the bed-stone; if it do, draw 
a little water, and let the stone move gently round; 
then see that all things be right, and draw a little more 
water, let the stone run at a moderate rate, and grind 
the faces a few minutes. 


ARTICLE 143. 

DIRECTIONS FOR MAKING A HOOP FOR THE MILL-STONE. 

Take a white pine or poplar board, 8 inches longer 
than will go round the stone, and 2 inches wider than 
the top of the stone is high, dress it smooth, and gauge it 
one inch thick, run a gauge mark ith of an inch from the 
outside, divide the length into 52 parts, and saw as many 
saw-gates square across the inside to the gauge-line. 
Take a board of equal width, 1 foot long, nail one-half 
of it on the outside at one end of the hoop, lay it in wa¬ 
ter a day or two to soak, or frequently sprinkle the out- 



CHAP. XXI.] OF FACING STONES, ETC. 319 

side with hot water, during an hour or two. Bend it 
round so that the ends meet and nail the other end to 
the short board, put sticks across the inside, in various 
directions, to press out the parts that bend least, and 
make it truly round. Make a cover for the hoop, (such 
as is represented in Plate XIX., fig. 23,) 8 square inside, 
and 1 inch outside the hoop. It consists of 8 pieces 
lapped one over another, the black lines showing the 
joints as they appear when made, the dotted lines the 
under parts of the laps. Describe it on the floor, and 
make a pattern to make all the rest by; dress all the 
laps, fit and nail them together by the circle on the 
floor, and then nail it on the hoop; put the hoop over 
the stone, and scribe it to fit the floor. 


ARTICLE 144. 

OP GRINDING SAND TO FACE THE STONES. 

Lay boards over the hoop to keep the dust from fly¬ 
ing, and take a bushel or two of dry, clean, sharp sand, 
teem it gently into the eye, while the stone moves at a 
moderate rate, continuing to grind for an hour or two: 
then take up the stones, sweep them clean, and pick the 
smoothest, hardest places, and lay the stone down again, 
and grind more sand as before, turning off the back, (if 
it be a burr,) taking care that the chisel do not catch; 
take up the stone again, and make a red staff equal in 
length to the diameter of the stone, and 3 by 21 inches; 
paint it with red paint and water, and rub it over the 
face of the stone in all directions, the red will be left 
on the highest and hardest parts, which must be picked 
down, making the bed-stone perfectly plain, and the 
runner a little concave, about 4th of an inch at the eye. 
and lessening gradually to about 8 inches from the skirt. 
If they be close and have much face, they need not 
touch, or flour, so far as if they be open, and have but 
little face; those things are necessarily left to the judg¬ 
ment of the mill-wright and miller. 



320 


OF FURROWING STONES. [CHAP. XXI. 


ARTICLE 145. 

DIRECTIONS FOR LAYING OUT THE FURROWS IN TILE STONES. 

If they be 5 feet in diameter, divide the skirt into 
1G equal parts, called quarters; if 6 feet, into 18; if 7 
feet, into 20 quarters. Make two strips of board, one 
an inch, and the other 2 inches wide; stand with your 
face to the eye, and if the stone turn to the right when 
at work, lay the strip at one of the quarter divisions; 
and the other at the left hand side, close to the eye, and 
mark with a Hat-pointed spike for a master furrow: they 
are all to be laid out the same way in both stones, 
for when their faces are together, the furrows should 
cross each other like shears in the best position for cut- 
ting«cloth. Then, having not fewer than G good picks, 
proceed to pick out all the master furrows, making the 
edge next the skirt and the end next the eye, the deep¬ 
est, and the feather edge not half so deep as the back. 

When all the master furrows are picked out, lay the 
broad strip next to the feather-edges of all the furrows, 
and mark the head lands of the short furrows, then lay 
the same strip next the back edges, and mark for the 
lands, and lay the narrow strip, and mark for the fur¬ 
rows, and so mark out all the lands and furrows, mind¬ 
ing not to cross the head lands, but leaving it between 
the master furroivs and the short ones of each quarter. 
But if they be close country stones, lay out both fur¬ 
rows and lands with the narrow strip. 

The neck of the spindle must not be wedged too tight, 
else it will burn loose; bridge the spindle again; put a 
collar round the spindle neck, but under it put a piece 
of an old stocking, with tallow rolled up in it, about a 
finger thick; tack it closely round the neck; put a piece 
of stiff leather about G inches diameter on the cock- 
liead, under the driver to turn with the spindle and 
drive off the grain, &c., from the neck; grease the neck 
with tallow every time the stone is up. 

Lay the stone down and turn off the back smooth, and 


321 


CHAP. XXI.] HOPPER, SHOE, AND FEEDER. 

grind more sand. Stop tlie mill, raise the stone a little, 
and balance it truly with a weight laid on the lightest 
side. Take lead equal to this weight, melt it, and run 
it into a hole made in the same place in the plaster; this 
hole should be largest at bottom, to keep it in; fill the 
hole with the plaster, take up the runner again, try the 
staff over the stones, and if in good face, give them a 
nice dressing, and lay them down to grind wheat. 


ARTICLE 140. 

DIRECTIONS FOR MAKING A HOPPER, SHOE, AND FEEDER. 

The dimensions of the hopper of a common mill are 4 
feet at the top, and 2 feet deep, the hole in the bottom 3 
inches square, with a sliding gate in the bottom of the 
front to lessen it at pleasure: the shoe ten inches long, 
and 5 wide in the bottom, of good sound oak. The side 
7 or 8 inches deep at the hinder end, 3 inches at the 
foremost end, G longer than the bottom of the fore end. 
slanting more than the hopper behind, so that it may 
have liberty to hang down 3 or 4 inches at the fore end. 
which is hung by a strap called the feeding string, pass¬ 
ing over the fore end of the hopper-frame, and lapping 
round a pin in front of the meal-beam, which pin will 
turn by the hand, and which is called the feeding-screw. 

The feeder is a piece of wood turned in a lathe, about 
20 inches long, 3 inches diameter in the middle, against 
the shoe, tapered off to IT inch at the top; the lower 
end is banded, and a forked iron driven in it, that spans 
over the ryne, fitting into notches made on each side, 
to receive it, directly above the spindle, with which it 
turns, the upper end running in a hole in a piece across 
the liopper-frame. In the large part, next the shoe, 6 
iron knockers are set, 7 inches long, half an inch dia¬ 
meter, with a tang at each end, turned square to drive 
into the wood; these knock against and shake the shoe, 
and thereby shake in the grain regularly. 

You may now put the grain into the hopper, draw wa¬ 
ter on the mill, and regulate the feed by turning the feed 
21 



322 OF BOLTING CHESTS, ETC. [CHAP. XXI. 

screw, until the stream falling into the eye of the stone 
be proportioned to the size thereof, or the power of the 
mill. Here ends the mill-wright’s work, with respect 
to grinding, and the miller takes the charge thereof. 


ARTICLE 147. 

OP BOLTING CHESTS AND REELS. 

Bolting chests and reels are of different lengths, ac¬ 
cording to the use for which they are intended. Com¬ 
mon country chests (a top view of one of which is shown 
in Plate XIX., fig. 9,) are usually about 10 feet long, 3 
feet wide, and 7 feet 4 inches high, with a post in each 
corner; the bottom 2 feet from the floor, with a board 
18 inches wide, set slanting in the back side, to cast the 
meal forward in the chest, that it may be easily taken up; 
the door is of the whole length of the chest, and two 
feet wide, the bottom board below the door sixteen 
inches wide. 

The shaft of the reel is equal in length with the chest, 
4 inches diameter, 6 square, two bands on each end, 31 
and 31 inches diameter: gudgeons 13 inches long, seven- 
eighths of an inch diameter, 8 inches in the shaft, rounded 
at the neck 21 inches, with a tenon for a socket, or handle; 
there are six ribs 11 inch deep, 1| inch thick, one-half 
an inch at the tail, and one and a half inch at the 
head, shorter than the shaft, to leave room for the meal 
to be spouted in at the head and the bran to fall out at 
the tail; there are four sets of arms, that is 12 of them, 
one and a half inch wide, and five-eighths thick. The 
diameter of the reel from out to out of the ribs, is one- 
third part of the double width of the cloth. A round 
wheel, made of inch boards, in diameter equal to the 
outside of the ribs, and 41 inches wide, measuring from 
the outside towards the centre, (which is taken out,) is 
to be framed to the head of the reel, to keep the meal 
from falling out at the head, unbolted. Put a hoop 
41 inches wide, and one-quarter thick, round the tail, 
to fasten the cloth to. The cloth is sewed, two widths 



CHAP. XXI.] BOLTS TO GO BY WATER. 323 

of it together, to reach round the reel, putting a strip of 
strong linen, 7 inches wide at the head, and 5 inches at 
the tail of the cloth, by which to fasten it to the reel. 
Paste on each rib a strip of linen, soft paper, or chamois 
leather, (which is the best) 1 h inch wide, to keep the 
cloth from fretting. Then put the cloth on the reel 
tight, sew or nail it to the tail, and stretch it length¬ 
wise as hard as it will bear, nailing it to the head.—Six 
yards of cloth cover a ten feet reel. 

Bolting reels for merchant mills are generally longer 
than for country work, and every part should be stronger 
in proportion. They are best when made to suit the 
wide cloths. The socket gudgeons at the head should 
be much stronger, they being apt to wear out, and trou¬ 
blesome to repair. 

The bolting-hopper is made to pass through the floor 
above the chest, is 12 inches square at the upper, and 10 
inches at the lower end; the foremost side 5 inches, and 
the back side 7 inches from the top of the chest. 

The shoe 2 feet long at the bottom of the side pieces, 
slanting to suit the hopper at the hinder end, set 4 inches 
higher at the hinder than the fore end, the bottom 17 
inches long, and 10 inches wide. There should be a bow 
of iron riveted to the fore end, to rest on the top of the 
knocking wheel, which is fixed on the socket gudgeon at 
the head of the chest, and is 10 inches diameter, 2 inches 
thick, with 6 half rounds, cut out of its circumference, 
forming knockers to strike against the bow, and lift the 
shoe I of an inch every stroke, to shake in the meal. 


ARTICLE 148. 

OF SETTING BOLTS TO GO BY WATER. 

The bolting reels are set to go by water as follows:— 
Make a bridge 6 by 4 inches, and 4 inches longer than 
the distance of the tomkin post, described Art. 139; set 
it between them, on rests fastened into them 10 inches 
below the cogs of the cog-wheel, and the centre of it half 
the diameter of the spur-wheel, in front of them; on this 
bridge is set the step gudgeon of an upright shaft, with 



324 


MAKING BOLTING WHEELS. [CHAP. XXI. 

a spur-wheel of 16 or 18 cogs to gear into the cog wheel. 
Fix a head-block to the joists of the 3d floor for the up¬ 
per end of this shaft; put the wheel 28, (PL XIX.) on it; 
hang another head-block to the joists of the 2d floor, near 
the corner of the mill at 6, for the step of the short up¬ 
right shaft that is to be fixed there, to turn the reels 1 
and 9. Hang another head-block to the joists'of the 3d 
floor, for the upper end of the said short upright, and fix 
also head-blocks for the short shaft at the head of the 
reels, so that the centres of all these shafts'will meet. 
Then fix a hanging post in the corner 5, for the gudgeon 
of the long horizontal shaft 27—5 to run in. After the 
head-blocks are all fixed, then measure the length of each 
shaft, and make them as follows; namely;— 

The upright shaft 51 inches for common mills, but if 
for merchant-work, with Evans’ elevators, &c., added, 
make it larger, say 6 or 7 inches; the horizontal shaft 27 
—5, and all the others 5 inches diameter. Put a socket- 
gudgeon in the middle of the long shafts, to keep them 
steady; make them 8, or 16, square, except at the end 
where the vdieels are hung, where they must be 4 square. 
Band their ends, put in the gudgeons, and put them in 
their proper places in the head-blocks, to mark w r here 
the wheels are to be put on them. 


ARTICLE 149. 

OF MAKING BOLTING WHEELS. 

Make the spur-wheel for the first upright with a 41 
inch plank; the pitch of the cogs the same as the cog¬ 
wheel into which it is to work; put two bands 1 of an 
inch wide, one on each side of the cogs, and a rivet be¬ 
tween each cog, to keep the wheel from splitting. 

To proportion the cogs in the wheels, to give the bolts 
the right motion, the common way is— 

Hang the spur-wheel, and set the stones to grind with 
a proper motion, and count the revolutions of the upright 
shaft in a minute; compare its revolutions with the revo¬ 
lutions that a bolt should have, which is about 36 revo¬ 
lutions in a minute. If the upright go one-sixth more, 



325 


CHAP. XXI.] MAKING BOLTING-WHEELS. 

put one-sixth less in the first driving wheel than in the 
leader; suppose 15 in the driver, then 18 in the leader: 
but if their difference be more, (say one-half,) there 
must be a difference in the next two wheels; observing 
that if the motion of the upright shaft be greater than 
that of the bolt should be, the driving wheel must be 
proportionally less than the leader: but if it be slower, 
then the driver must be greater in proportion. The com¬ 
mon size of bolting wheels is from 14 to 20 cogs; if less 
than 14, the head-blocks will be too near the shafts. 

Common bolting wheels should be made of plank, at 
least 3 inches thick, well seasoned; and they are best 
when as wide as the diameter of the wheel, and banded 
with bands nearly as wide as the thickness of the wheel; 
the bands may be made of rolled iron, about one-eighth 
of an inch thick. Some make the wheels of 2 inch plank, 
crossed, and no bands; but this proves no saving, as they 
are apt to go to pieces in a few years. (For hooping 
wheels, see Art. 136, and for finding the diameter of the 
pitch circle, see Art. 126.) The wheels, if banded, are 
generally two inches more in diameter than the pitch 
circle; but if not, they should be larger. The pitch or 
distances of the cogs are different; if to turn 1 or 2 bolts, 
21 inches, but, if more, 21; if they are to do much heavy 
work, they should not be less than 3 inches. Their 
cogs, in thickness, are half the pitch: the shank must 
drive tightly in an inch auger hole. 

When the mortises are made for the shafts in the 
head, and notches for the keys to hang them, drive the 
cogs in and pin tlieir shanks at the back side, and cut 
them off half an inch from the wheel. 

Hang the wheels on the shafts so that they will gear 
a proper depth, about two-thirds the thickness of the 
cogs; dress all the cogs to equal distances by a gauge; 
then put the shafts in their places, the wheels gearing 
properly, and the head-blocks all secure; set them in 
motion by water. Bolting reels should turn so as to 
drop the meal on the back side of the chest, as it will 
then hold more, and will not cast out the meal when 
the door is opened. 


32G 


OF ROLLING-SCREENS. 


[CHAP. XXI. 


ARTICLE 150. 

OF ROLLING-SCREENS. 

These are circular sieves, moved by water, and are 
particularly useful in cleaning wheat for merchant-work. 
They are of different constructions. 

1st. Those of one coat of wire with a screw in them. 

2dly. Those of two coats, the inner one nailed to six 
ribs, the outer one having a screw between it and the 
inner one. 

3dly. Those of a single coat, and no screw. 

The first kind answers well in some, but not in all 
cases, because they must turn a certain number of times 
before the wheat can get out, and the grain has not so 
good an opportunity of separating; there being nothing 
to change its position, it floats a considerable distance 
with the same grains uppermost. 

The double kinds are better, because they may be 
shorter and take up less room, but they are more diffi¬ 
cult to keep clean. 

The 3d kind has this advantage; we can keep the 
grain in them a longer or shorter time, at pleasure, by 
raising or lowering the tail end, and it is also tossed 
about more; but they must be longer. They are gene¬ 
rally 9 or 10 feet long, 2 feet 4 inches diameter, if to 
clean for two or three pairs of stones; but if for more, 
they should be larger accordingly: they will clean for 
from one to six pairs of stones. They are made G square, 
with G ribs, which lie flatwise, the outer corner taken 
off to leave the edges one quarter of an inch thick; the 
inner corners are brought nearly to sharp edges; the 
wire work is nailed on with 14 ounce tacks. 

The screens are generally moved by the same upright 
shaft that moves the bolts, which has a wheel on its up¬ 
per end, with two sets of cogs: those that strike down¬ 
wards gear into a wheel striking upwards, which turns 
a laying shaft, having two pulleys on the other end, one 
of 24 inches diameter, to turn a fan with a quick motion, 
the other of 8 inches, which conducts a strap to a pulley, 


OF FANS, ETC. 


CHAP. XXI.] 


327 


24 inches diameter, on the gudgeon of the rolling screen, 
to reduce its motion to about 15 revolutions in a minute. 
(See fig. 19, Plate XIX.) This strap gearing may do 
for mills in a small way, but where they are in perfec¬ 
tion for merchant work, with elevators, &c., and have to 
clean wheat for two, three, or four pairs of stones, thev 
should be moved by cogs. 


ARTICLE 151. 

OF FANS. 

The Dutch fan is a machine of great use for blowing 
the dust and other light stuff from among the wheat; 
there are various sorts of them; those that are only for 
blowing the wheat as it falls from the rolling-screen, 
are generally about 15 inches long and 14 inches wide 
in the wings, and have no riddle or screen in them. 

To give motion to a fan of this kind, put a pulley 7 
inches diameter, on its axle, to receive a band from a 
pulley on the shaft that moves the screen, which pulley 
may be of 24 inches diameter, to give a swift motion; 
when the band is slack it slips a little on the small pul¬ 
ley, and the motion is retarded, but when tight the mo¬ 
tion is quicker; by this the blast is regulated. 

Some use Dutch fans complete, with riddle and screen 
under the rolling screen, for merchant-work; and again 
use the fan alone for country work. 

TJie wings of those which are the common farmers’ 
wind-mills, or fans, are 18 inches long and 20 inches 
wide; but in mills they are set in motion with a pulley 
instead of a cog-wheel and wallower. 


ARTICLE 152. 

OF THE SHAKING SIEVE. 

Shaking sieves are of considerable use in country 
mills, to sift Indian meal, separating it, if required, into 




328 


OF THE SHAKING SIEVE. [CIIAP. XXI. 

several degrees of fineness; and to take tlie hulls out of 
buckwheat meal, which are apt to cut the bolting-cloth; 
also, to take the dust out of the grain, if rubbed before 
ground: they are sometimes used to clean wheat or 
screenings, instead of rolling-screens. 

If they are for sifting meal, they are 3 feet 6 inches 
long, 9 inches wide, 31 inches deep, (see it, fig. 16, Plate 
XVIII.) The wire-work is 3 feet long, and 8 inches 
wide: across the bottom of the tail end is a board six 
inches wide, to the top of which the wire is tacked, and 
then this board and wire are tacked to the bottom of the 
frame, leaving an opening at the tail end for the bran 
to fall into the box 17, the meal falling into the meal- 
trough 15: the head piece should be strong to hold the 
iron bow at 15, through which the lever passes that 
shakes the sieve, which is effected in the following man¬ 
ner. Take two pieces of hard wood, 15 inches long, and 
as wide as the spindle, and so thick that when one is 
put on each side just above the trundle, it will make it 
one and a half inches thicker than the spindle is wide. 
The corners of these are taken off to a half round, and 
they are tied to the spindle with a small strong cord. 
These are to strike against the lever that works on a 
pin near its centre, which is fastened to the sieve and 
shakes it as the trundle goes round; (see it represented 
Plate XVIII.) This lever must always be put to the 
side of the spindle, contrary to that of the meal-spout; 
otherwise, it will draw the meal to the upper end of the 
sieve: there must be a spring fixed to the sieve to draw 
it forward as often as it is driven back. It must bans: 

c 

on straps, and be fixed so as to be easily set to any de¬ 
scent required, by means of a roller in the form of a 
feeding screw, only longer; round this roller the strap 
winds. 

I have now given directions for making and putting 
to work all the machinery of one of the most complete 
of the old-fashioned grist-mills, that may do merchant- 
work in the small way; these are represented by Plates 
XVIII:, XIX., XX., XXL; but they are far inferior to 
those with the improvements, which are shown by Plate 
XXII. 


CHAP. XXII.] TJSE OF DRAUGHT MILLS. 

V 

b rAR 

CHAPTER XXII. 



329 


ARTICLE 153. 

OF THE USE OF DRAUGHTING TO BUILD MILLS BY, ETC. 

Perhaps some are of opinion that draughts are useless 
pictures of things, serving only to please the fancy. 
This is not what is intended by them; hut to give true 
ideas of the machine, &c., described, or to he made. 
Those represented in the plates are all drawn on a scale 
of one-eighth of an inch to a foot, in order to suit the size 
of the hook, except Plate XVII., which is a quarter of 
an inch to a foot; and this scale I recommend, as most 
buildings will then come on a sheet of common paper. 

N. B.—Plate XXIV. was made after the above di¬ 
rections, and has explanations to suit it. 

The great use of draughting mills, &c., to build by, 
is to convey our ideas more plainly than is possible by 
writing, or by words alone; these may be misconstrued 
or forgotten; but a draught well drawn, speaks for itself, 
when once understood by the artist; who, by applying 
his dividers to the draught and to the scale, finds the 
length, breadth, and height of the building, or the di¬ 
mensions of any piece of timber, and its proper place. 

By the draught, the bills of scantling, boards, rafters, 
laths, shingles, &c., &c., are known and made out; it 
should show every wheel, shaft and machine, and their 
jDlaces. By it we can find whether the house be suffi¬ 
cient to contain all the works that are necessary to carry 
on the business; the builder or owner understands what 
he is about, and proceeds cheerfully and without error. 
It directs the mason where to put the windows, doors, 
navel-holes, the inner walls, &c., whereas, if there be no 
draught, every thing goes on, as it were, in the dark; 
much time is lost, and errors are committed to the loss of 
many pounds. I have heard a man say that he believed 
his mill was 500/. better from having employed an expe¬ 
rienced artist to draw him a draught to build it by; and 
I know, by experience, the great utility of them. Every 
master builder, at least, ought to understand them. 



330 PLANNING AND DRAUGHTING. [CHAP. XXII- 


ARTICLE 154. 

DIRECTIONS FOIl PLANNING AND DRAUGHTING MILLS. 

1st. If it be a new seat, view the ground where the 
dam is to be, and where the mill-house is to stand, and 
determine on the height of the top of the water in the 
head race, where it is taken out of the stream; aud le¬ 
vel from it for the lower side of the race, down to the 
seat of the mill-house, and mark the level of the water 
in the dam there. 

2nd. Begin where the tail-race is to empty into the 
stream, and Jevel from the top of the water up to the 
mill seat, noticing the depth thereof in places, as you 
pass along, which will be of use in digging it out. 

Then find the total fall, allowing one inch to a rod 
for fall in the races; but if they be very wide and long, 
less will do. 

Then, supposing the fall to be 21 feet 9 inches, which 
is sufficient for an overshot mill, and the stream too light 
for an undershot, consider well what size stone will suit; 
for I do not recommend a large stone to a weak, nor a 
small one to a strong stream. I have proposed stones 4 
feet diameter for light, 4.G for middling, and 5 or 5 feet 
6 inches diameter, for heavy streams. Suppose you de¬ 
termine on stones 4 feet, then look in table I., (which is 
for stones of that size,) column 2, for the fall that is 
nearest 21 feet 9 inches, your fall, and you find it in the 
7th example. Column 3d contains the head of water 
over the wheel, 3 feet; 4th, the diameter of the wheel, 
18 feet; 5tli, its width, 2 feet 2 inches, &c., for all the 
proportions to make the stone revolve 10G times in a 
minute. 

Having determined on the size of the wheels, and also 
of the house; the heights of the stories, to suit the wheels 
and machinery it is to contain, and the business to be 
carried on therein, proceed to draw a ground plan of the 
house, such as plate XVIII., which is 32 by 55 feet. (See 
the description of the plate.) And for the second story, 
as plate XIX., &c., and for the 3d, 4tli and 5th floors, if 


CHAP. XXII.] BILLS OF SCANTLING. 331 

required; taking care to plan every tiling so that one 
shall not clash with another. 

Draw an end view, as Plate XX., and a side view, as 
Plate XXI. Take the draught to the ground, and stake 
out the seat of the house. It is in general best to set 
that corner of an overshot mill, at which the water en¬ 
ters, farthest in the bank; but great care should be 
taken to reconsider and examine every thing, more than 
once, to see whether it be planned for the best; because, 
much labour is often lost for want of due consideration, 
and by setting buildings in, and laying foundations on, 
wrong places. The arrangements being completed, the 
bills of scantling and iron work may be made out from 
the draught. 


ARTICLE 155. 

BILLS OF SCANTLING FOR A MILL THIRTY-TWO BY FIFTY-FIVE FEET, 

THREE STORIES HIGH-THE WALLS OF MASON WORK, SUCH AS IS 

REPRESENTED IN PLATES XVIII., XIX., XX., AND XXI. 

For the first Floor . 

2 sills, 29 feet long, 8 by 12 inches, to lay on the walls 
for the joists to lie on. 

48 joists, 10 feet long, 4 by 9 inches, all of timber that 
will last well in damp places. 

For the second Floor . 

2 posts, 9 feet long, 12 by 12 inches. 

2 girders, 30 feet long, 14 by 1G do. 

48 joists, 10 feet long, 4 by 9 do. 

For the floor over the water-house. 

1 cross girder, 30 feet long, 12 by 14 inches, for one end 
of the joists to lie on. 

2 posts to support the girder, 12 feet long, 12 by 12 
inches. 

1G joists, 13 feet long, 4 by 9 inches; all of good white 
oak, or other timber that will last in damp places. 



332 


BILLS OF SCANTLING. 


[CHAP. XXII. 


For the third floor. 

4 posts, 9 feet long, 12 by 12 inches, to support the 
girders. 

2 girder posts, 7 feet long, 12 by 12 inches, to stand on 
the water-house. 

2 girders, 53 feet long, 14 by 1G inches. 

90 joists, 10 feet long, 4 by 9 inches. 

For the fourth floor. 

G posts, 8 feet long, 10 by 10 inches, to support the 
girders. 

2 girders, 53 feet long, 13 by 15 inches. 

30 joists, 10 feet long, 4 by 8 do., for the middle tier of 
the floor. 

GO joists, 12 feet long, 4 by 8, for the outside tiers, which 
extend 12 inches over the walls, for the rafters to 
stand on. 

2 plates, 54 feet long, 3 by 10 inches: these lie on the 
top of the walls, and the joists on them. 

2 raising pieces, 55 feet long, 3 by 5 inches; these lie on 
the ends of the joists for the rafters to stand on. 

For the roof. 

54 rafters, 22 feet long, 3 inches thick, G? wide at the 
bottom, and 41 at the top end. 

25 collar beams, 17 feet long, 3 by 7 inches. 

27G0 feet of laths, running measure. 

7000 shingles. 

For doors and window-cases. 

12 pieces, 12 feet long, G by G inches, for door-cases. 

3G do., 8 feet long, 5 by 5 inches, for window-cases. 

For the water-house. 

2 sills, 27 feet long, 12 by 12 inches. 

1 do., 14 feet long, 12 by 12 do. 

2 spur-blocks, 4 feet G inches long, 7 by 7 do. 

2 head-blocks, 5 feet long, 12 by 14 do. 

4 posts, 10 feet long, 8 by 8, to bear up the penstock. 

2 cap-sails, 9 feet long, 8 by 10, for the penstock to 
stand on. 


LC tsL tC 1C 1C C’i LC LO 1C ^ 1C 


BILLS OF SCANTLING. 


CHAP. NXII.] 


ooo 


4 corner posts, 5 feet long, 4 by 6 inches, for tlie corners 
of the penstock. 


For the husk of a mill of one water-wheel and two pairs of 

stones. 

sills, 24 feet long, 12 by 12 inches, 
corner posts, 7 feet long, 12 by 14 inches, 
front posts, 8 feet long, 8 by 12 do. 
back posts, 8 feet do., 10 by 12 inches, to support the 
back ends of the bridge-trees, 
other back posts, 8 feet long, 8 by 8 inches, 
tomkin-posts 12 feet long, 12 by 14 do 
interties, 9 feet long, 12 by 12 inches, for the outer 
ends of the little cog-wheel shafts to rest on. 
top pieces, 10 feet 6 inches long, 10 by 10 inches, 
beams, 24 feet long, 16 by 16 inches, 
bray-trees, 81 feet long, 6 by 12 inches, 
bridge-trees, 9 feet long, 10 by 10 inches, 
planks, 8 feet long, 6 by 14 inches, for the stone-bearers. 
20 planks, 9 feet long, 4 by about 15 inches, for the top 
of the husk. 

2 head-blocks, 7 feet long, 12 by 15 inches, for the wal- 
lower shafts to run on. They serve as spurs also for 
the head-block for the water-wheel shaft. 


For the ivater-wheel and big cog-w'heel. 

1 shaft, 18 feet long, 2 feet diameter. 

8 arms for the water-wheel, 18 feet long, 3 by 9 inches. 
16 shrouds, 82 feet long, 2 inches thick and 8 deep. 

16 face boards, 8 feet long, 1 inch thick and 9 deep. 

56 bucket boards, 2 feet! inches long and 17inches wide. 
140 feet of boards, for soaling the wheel. 

3 arms for the cog-wheel, 9 feet long, 4 by 14 inches. 
16 cants, 6 feet long, 4 by 17 inches. 


For little cog-wheels. 

2 shafts, 9 feet long, 14 inches diameter. 
4 arms, 7 feet long, 31 by 10 inches. 

16 cants, 5 feet long, 4 by 18 inches. 


334 


BILL OF LARGE IRONS, ETC. [CIIAF. XXII. 


For wallowers and trundles. 

60 feet of plank, 31 inches thick. 

40 feet do., 3 niches thick, for bolting gears. 

Cogs and rounds. 

200 cogs, to be split, 3 by 3, 14 inches long. 

80 rounds, do., 3 by 3, 20 inches long. 

160 cogs, for bolting works, 7 inches long, and If square; 
but if they be for a mill with machinery complete, 
there must be more in number, accordingly. 

Bolting shafts . 

1 upright shaft, 14 feet long, 51 by 51 inches. 

2 horizontal shafts, 17 feet long, 5 by 5 inches. 

1 upright do. 12 feet long, 5 by 5 inches. 

6 shafts, 10 feet long, 4 by 4 do. 


ARTICLE 156. 

BILL OF THE LARGE IRONS FOR A MILL OF TWO PAIRS OF STONES. 

2 gudgeons, 2 feet 2 inches long in the shaft; neck 41 
inches long, 3 inches diameter, ivell steeled and turned. 
(See fig. 16, Plate XXIV.) 

2 bands, 19 inches diameter inside, three quarters thick, 
and 3 inches wide for the ends of the shaft. 

2 do.. 201 inches inside, half an inch thick, and 21 
inches wide, for do. 

2 do., 23 inches do., half an inch thick, and 21 inches 
wide, for do. 

4 gudgeons, 16 inches in the shaft, 31 inches long, and 
21 inches diameter in the neck, for wallower shafts; 
(See fig. 15, Plate XXIV.) 

4 bands, 12 inches diameter inside, half an inch thick, 
and 2 wide, for do. 

4 do., 12 inches do., half an inch thick, and 2 wide, for do. 

4 wallower bands, 3 feet 2 inches diameter inside, 3 
inches wide, and quarter of an inch thick. 

4 trundle bands, 2 feet diameter inside, 3 inches wide, 
and quarter of an inch thick. 



CIIAP. XXII.] BILL OF IRON. 335 

2 spindles and rynes; spindles 5 feet 3 inches long from 
the foot to the top of the necks; cock-heads 7 or 8 
inches long above the necks; the body of the spin¬ 
dles 3i by 2 inches; the neck three inches long and 
3 inches diameter; the balance rynes proportional to 
the spindles, to suit the eye of the stone, which is 9 
inches diameter. (See figs. 1, 2, 3, Plate XXIV.) 

2 steps for the spindles, fig. 4. 

2 sets of damsel-irons, 6 knockers to each set. 

2 bray-irons, 3 feet long, If inch wide, half an inch 
thick; being a plain bar, one hole at the lower, and 
5 or 6 at the upper end. 

Bill of iron for the bolting and hoisting works , in the common 

way. 

2 spur-wheel bands, 20 inches diameter from outsides 
for the bolting spur-wheel, three-fourths of an inch 
wide, and one-fourth thick. 

2 spur-wheel bands, 12 inches diameter from outsides, 
for the hoisting spur-wheel. 

2 step-gudgeons and steps, 10 inches long, one and one- 
eighth inch thick in the tang or square part; neck 3 
inches long, for the upright shafts. (See fig. 5 and 0. 
Plate XXIV.) 

2 bands for do., 5 inches diameter inside, one and a quar¬ 
ter wide, and one and a quarter thick. 

2 gudgeons, 9 inches tang, neck 3 inches long, one and 
one-eighth square, for the top of the uprights. 

8 bands, 41 inches diameter inside. 

1 socket gudgeon, one and one-eighth of an inch thick, 
tang 12 inches long, neck 4 inches, tenon, to go into 
socket, one and a half inch, with a key-hole at the 
end. (See figs. 8 and 9.) 

14 gudgeons; neck 21 inches, tangs 8 inches long, and 
one inch square, for small shafts at one end of the 
bolting-reels. 

10 bands for do. 4 inches diameter inside, and 1 inch wide. 

4 socket-gudgeons, for the 4 bolting-reels, one and a quar¬ 
ter square; tangs 8 inches, necks 3 inches, and tenons 
one and a half inch with holes in the ends of the tangs 
for rivets, to keep them from turning; the sockets 
one inch thick at the mortise, and 3 inches between 


336 EXPLANATION OF PLATES. [CHAP. XXII. 

the prongs. (See figs. 8 and 9.) Prongs 8 inches 
long and one wide. 

8 bands, 31 inches, and 8 do., 4 inches diameter, for the 
bolting-reel shafts. 


For the hoisting wheels. 

2 gudgeons, for the jack-wheel, neck 31 inches, and tang 
9 inches long, one and one-eighth square. 

2 bands for do., 4-1 inches diameter. 

2 gudgeons, for the hoisting wheel, neck 31 inches, tang 
9 inches long, and one and a quarter inch square. 

2 bands for do., 7 inches diameter. 

6 bands for bolting-heads, 10 inches diameter inside, 21 
wide, and one-sixtli of an inch thick. 

G do. for do., 15 inches do., do. 

N. B.—Ail the gudgeons should taper a little, and the 
sides given are the largest part. The bands for shafts 
should be widest at the foremost side, to make them 
drive well; but those for heads should be both sides 
equal. Six picks for the stones, 8 inches long and one 
and a quarter wide, will be wanted. 


ARTICLE 157. 

EXPLANATION OF THE PLATES. 

PLATE XVII. 

Drawn from a scale of a quarter of an inch for a foot. 
Fig. 1—a big cog-wheel, 8 feet 21 inches the diameter 
of its pitch circle, 8 feet 101 inches from out to out; 
69 cogs, 41 inches pitch. 

2— a little cog-wheel, 5 feet 101 inches the diameter of 
its pitch circle, and G feet G inches from out to out. 
to have 52 cogs, 41 pitch. 

3— a wallower, 3 feet 11 inches the diameter of its 
pitch circle, and 3 feet 41 inches from out to out; 2G 
rounds, 41 pitch. 

4— a trundle, 1 foot 81 inches the diameter of its pitch 
circle, and 1 foot 111 inches from out to out; 15 
rounds, 41 inches pitch. 

5— the back part of the big cog-wheel. 




337 


CHAP. XXII.] EXPLANATION OF PLATES. 

G—a model of locking 3 arms together. 

7—the plan of a forebay, showing the sills, caps and 
where the mortises are made for the posts, with a rack 
at the upper end to keep off the trash. 


PLATE XVIII.— The ground part of a mill. 

Fig. 1 and 8—bolting chests and reels, top view. 

2 and 4—cog-wheels that turn the reels. 

3—cog-wheel on the lower end of a short upright shaft. 
5 and 7—places for the bran to fall into. 

6, G, 6—three garners on the lower floor for bran. 

9 and 10—posts to support the girders. 

11— the lower door to load wagons, horses, &c., at. 

12— the step-ladder, from the lower floor to the husk. 

13— place where the hoisting casks stand when filling. 

14 and 15—the two meal-troughs and meal spouts. 

1G—meal-shaking sieve for Indian and buckwheat. 

17—a box for the bran to fall into from the sieve. 

18 and 19—the head-block and long spur-block, for the 
big shaft. 

20— four posts in front of the husks, called bray posts. 

21— the water and cog-wheel shaft. 

22— the little cog-wheel and shaft, for the lower stones. 

23— the trundle for the burr stones. 

24— the wallower for do 

25— the spur-wheel that turns the bolts. 

26— the cog-wheel. 

27— the trundle, head wallower, and bridge-tree, for 
country stones. 

28— the four back posts of the husk. 

29— the two posts that support the cross-girder. 

30— the two posts that bear up the penstock at one side. 

31— the water-wheel, 18 feet diameter. 

32— the two posts that bear up the other side of the 
penstock. 

33— the head-blocks and spur-blocks, at water end. 

34— a sill to keep up the outer ends. 

35— the water-house door. 

36— a hole in the wall for the trunk to go through. 

37— the four windows of the lower story. 

22 

JmJ — 





338 


EXPLANATION OF PLATES. [CIIAP. XXII. 

PLATE XIX .—Second floor. 

Fig. 1 and 9—a top view of the bolting chests and reels. 

2 and 10—places for the bran to fall into. 

3 and 8—the shafts that turn the reels. 

4 and 7—wheels that turn the reels. 

5— a wheel on the long shafts between the uprights. 

6— a wheel on the upper end of the upright shaft. 

11 and 12—two posts that bear up the girders of the 
third floor. 

13— the long shaft between two uprights. 

14— five garners to hold toll, &c. 

15— a door in the upper side of the mill-house. 

16— a step-ladder from second to third floor. 

17— the running burr mill-stone laid off to be dressed. 

18— the hatch-way. 

19— stair-way. 

20— the running country stone turned up to be dressed. 

21— a small step-ladder from the husk to the second 
floor. 

22— the places where the cranes stand. 

24—the pulley-wheel that turns the rolling screen. 

25 and 26—the shaft and wheel which turn the rolling 
screen and fan. 

27— the wheel on the horizontal shaft to turn the bolt¬ 
ing reels. * 

28— the wheel on the upper end of the first upright 
shaft. 

29— a large pulley that turns the fan. 

30— the pulley at the end of the rolling screen. 

31— the fan. • ‘ * 

32— the rolling screen. 

33— a step-ladder' from the husk to the lloor over the 
water-house. 

34 and 35—two posts that support the girders of the 
third floor. 

36— a small room for the tailings of the rolling screen. 

37— a room for the fannings. 

38— a room for the screenings. 

39— a small room for the dust. 

40— the penstock of water. 

41— a room for the miller to keep his books in. 





339 


CHAP. XXII.] EXPLANATION OF PLATES. 

42— a fire place. 

43— the upper end door. 

44— ten windows in the second story, twelve lights each. 

PLATE XX. 

Represents a view of the lower side of a stone mill- 
house, three stories high, which plan will suit tolerably 
well for a two story house, if the third story be not 
wanted. Part of the wall is supposed to be open, so 
that we have a view of the stones, running gears, &c. 
Line 1 represents the lower floor, and is nearly level 
with the top of the sills, of the husk and water-house. 
2, 3, and 4—the second, third and fourth floors. 

5 and G—windows for admitting air under the lower 
floor. 

7— the lower door, with steps to ascend to it, which 
commonly suits best to load from. 

8— the arch over the tail race for the water to run 
from the wheel. 

9— the water-house door, which sometimes suits better 
to be at the end of the house, where it makes room 
to wedge the gudgeon. 

10— the end of the water-wheel shaft. 

11— the big cog-wheel shaft. 

12— the little cog-wheel and wallow^er, the trundle be¬ 
ing seen through the window. 

13— the stones with the hopper, shoe, and feeder, as 
fixed for grinding. 

14— the meal-trough. 

There is an end view of the husk frame. There are 
thirteen windows with twelve lights each. 

PLATE XXI. 

Represents an outside view of the water-end of a mill- 
house, and is intended to show to the builders and mill¬ 
wrights, the height of the walls, floors and timbers, with 
the places of the doors and windows, and a view of the 
position of the stones and husk timbers, supposing the 
wall open, so that we could see them. 

Figs. 1, 2, 3, and 4, show the joists of the floors. 




340 


OF SAW-MILLS. 


[CHAP. XXIII. 


5— a weather-cock, turning on an iron rod. 

6— the end of the shaft, for hoisting outside of the house, 
which is fixed above the collar beams over the doors, 
to hoist into either of them, or either story, at either 
end of the house, as may suit best. 

7— the dark squares, showing the ends of the girders. 

8— the joists over the water-house. 

9— the mill-stones, with the spindles they run on, and 
the ends of the bridge-trees, as they rest on the brays 
aa, bb show the ends of the brays that are raised and 
lowered by the levers cc, called the lighter-staffs, for 
raising and lowering the running stone. 

10— the water-wheel and big cog-wheel. 

11— the wall between the water and cog-wheel. 

12— the end view of the two side walls of the house. 
Plate XXII. is explained in the preface. 


CHAPTER XXIII. 

ARTICLE 158. 

OF SAW-MILLS. 

Construction of their water-wheels. 

The wheels for saw-mills have been variously con¬ 
structed ; the most simple, where water is plenty, and 
the fall above six feet, is the flutter-wheel; but where 
water is scarce, or the head insufficient to give flutter- 
wheels the requisite motion, high wheels, double-geared, 
will be found necessary. Flutter-wheels may be adapted 
to any head above six feet, by making them low and 
wide for low heads, and high and narrow for high ones, 
so as to have about 120 revolutions, or strokes of the 
saw in a minute: but rather than double gear, I would 
be satisfied with 100. 



CHAP. XXIII.] 


OF SAW-MILLS. 


341 


A TABLE 


OF THE 

DIAMETER OF FLUTTER-WHEELS FROM OUT TO OUT, AND THEIR 
WIDTH IN THE CLEAR, SUITABLE TO ALL HEADS, FROM SIX TO 
THIRTY FEET. 


% 

Head of water. 

Diameter. 

Width. 

feet. 

ft. in. 

ft. in. 

6 

2 : 8 

5 : 6 

7 

2 : 10 

5 : 0 

8 

2 : 11 

4 : 8 

9 

3 : 0 

4 : 3 

10 

3: 1 

4 : 0 

11 

3 : 2 

3 : 9 

12 

3 : 3 

3 : 6 

13 

3 : 4 

3 : 3 

14 

3 : 5 

3 : 0 

15 

.3 : 6 

2 : 9 

16 

3 : 7 

2 : 6 

17 

3 : 8 

2 : 4 

18 

3 : 9 

2 : 2 

19 

3 : 10 

2 : 0 

20 

3 : 11 

I : 10 

21 

4 : 0 

1 : 9 

22 

4 : 1 

1 : 8 

23 

4 : 2 

1 : 7 

24 

4:3 

1 : 6 

25 

4 : 4 

1 : 5 

26 

4 : 5 

1 : 4 

# 27 

4 : 6 

1 : 3 

28 

4 : 7 

1 : 2 

29 

4 : 8 

1 : 1 

30 

4 : 9 

1 : 0 


N. B.—The above wheels are proposed to be made as narrow as will well do, 
on account of saving water; but if this be abundant the wheels may be made 
wider than directed in the table, and the mill will be the more powerful. 




























342 


OF SAW-MILLS. 


[CHAP. XXIII. 


Of geared saic-?nills. 

Of these I shall say but little, they being expensive 
and but little used. They should be geared so as to 
give the saw 120 strokes in a minute, when at work in 
a common log. The water-wheel is like that of any 
other mill, whether of the overshot, undershot, or breast 
kind; the cog-wheel of the spur kind, and as large as 
will clear the water. The wallower commonly has 14 
or 15 rounds, or such number as will produce the right 
motion. On the wallower shaft is a balance-wheel, 
which may be made of stone or wood: this is to regu¬ 
late the motion. There should be a good head above 
the water-wheel to give it a lively motion, otherwise the 
mill will run heavily. 

The mechanism of a complete saw-mill is such as to 
produce the following effects, namely:— 

1. To move the saw up and down with a sufficient 
motion and power. 

2. To move the log to meet the saw. 

3. To stop of itself when within 3 inches of being 
through the log. 

4. To draw the carriage with the log back, by the 
power of the water, so that the log may be ready to 
enter again. 

The mill is stopped as follows, namely:—When the 
gate is drawn the lever is held by a catch, and there is 
a trigger, one end of which is within half an inch of the 
side of the carriage, on which is a piece of wood an inch 
and a half thick, nailed so that it will catch against the 
trigger as the carriage moves, which throws the catch 
off the lever of the gate, and it shuts down at a pro¬ 
per time. 

Description of a saw-mill. 

Plate XXIII. is an elevation and perspective view of 
a saw-mill, showing the foundation, walls, frame, &c., &c. 

Fig. 0, 1—the frame uncovered, 52 feet long, and 12 
feet wide. 

Fig. 2—the lever for communicating the motion from 


OF SAW-MILLS. 


CHAP. XXIII.] 


o A O 
0^:0 


the saw-gate to the carriage, to move the log; it is 8 feet 
long, 3 inches square, tenoned into a roller 6 inches 
diameter, reaching from plate to plate, and working on 
gudgeons in them; in its lower side is framed a block, 10 
inches long, with a mortise in it two inches wide through¬ 
out its whole length, to receive the upper end of the hand 
pole, having in it several holes for an iron pin, to join 
the hand pole to it, to regulate the feed; by setting the 
hand pole nearer the centre of the roller, less feed is 
given, and, farther off, gives more. 

Fig. 3, the hand pole or feeder, is 12 feet long and 3 
inches square, where it joins the block, (Fig. 4,) and 
tapering 2 inches at the lower end, on which is the iron 
hand, 1 foot long, with a socket; the end of this is flat¬ 
tened, steeled, and hardened, and turned down half an 
inch at each side, to keep it on the rag-wheel. 

Fig. 5—the rag-wheel. This has four cants, 41 feet 
long, 17 by 3 inches in the middle, lapped together to 
make the wheel 5 feet diameter; is faced between the 
arms with two inch plank, to strengthen the laps. The 
cramp or ratchet iron is put on as a hoop, nearly 1 inch 
square, with ratchet notches cut on its outer edge, about 
3 to an inch. On one side of the wheel are put 12 strong 
pins 9 inches long, to tread the carriage back, when the 
backing works are out of order. On the other side are 
the cogs, about 56 in number, 3 inches pitch, to gear into 
the cog-wheel on the top of the tub-wheel shaft, with 15 
or 16 cogs. In the shaft of the rag-wheel are 6 or 7 
rounds, 11 inches long in the round part, let in nearly 
their whole thickness, so as to be of a pitch equal to the 
pitch of the cogs of the carriage, and gear into them 
easily: the ends are tapered off outside, and a band is 
driven on them at each end, to keep them in their places. 

Fig. 6 is the carriage; a frame 4 feet wide from out¬ 
sides, one side 29 feet long, 7 by 7 inches; the other 32 
feet long, 8 by 7 inches, very straight and true, the in¬ 
terties at each end 15 by 4 inches, strongly tenoned and 
braced into the sides to keep the frame from racking. In 
the underside of the largest piece are set two rows of 
cogs, 2 inches between the rows, and 9 inches from the 


344 OF SAW-MILLS. [ciiap. XXIII. 

foreside of one cog to that of another; the cogs ol one 
row between those of the other, so as to make 4 4 inches 
pitch, to gear into the rounds of the rag-wheel. The 
cogs are about 66 in number; shank 7 inches long, 1| 
inch square; head 21 long, 2 inches thick at the points, 
and 24 inches at the shoulder. 

Fig. 7—the ways for the carriage to run on. These 
are strips of plank 4 4 inches wide, 2 inches thick, set on 
edge, let 14 inch into the top of the cross sills, of the 
whole length of the mill, keyed fast on one side, made 
very straight both side and edge, so that one of them 
will pass easily between the rows of cogs in the carriage, 
and leave no room for it to move sidewise. They should 
be of hard wood, well seasoned, and hollowed out between 
the sills to keep the dust from lodging on them. 

Fig. 8—the fender posts. The gate with the saw 
plays in rabbets 24 deep and 4 inches wide, in the fen¬ 
der posts, which are 12 feet long, and 12 inches square, 
hung by hooked tenons to the front side of the two large 
cross beams in the middle of the frame, in mortises in 
their upper sides, so that they can be moved by keys to 
set them plumb. There are 3 mortises, 2 inches square, 
through each post, within half an inch of the rabbets, 
through which pass hooks with large heads, to keep the 
frame in the rabbets: they are keyed at the back of the 
posts. 

Fig. 9—the saw, which is 6 feet long, 7 or 8 inches 
wide, when new; hung in a frame 6 feet wide from the 
outsides, 6 feet 3 inches long between the end pieces, the 
lowermost of which is 14 by 3 inches, the upper one 12 
by 3, the side pieces 5 by 3 inches, 10 feet long, all of 
the best dry, hard wood. The saw is fastened in the 
frame by two irons, in form of staples; the lower one 
with two screw pins passing through the lower end. 
screwing one leg to each side of the end piece: the legs 
of the upper one are made into screws, one at each side 
of the end piece, passing through a broad, flat bar, that 
rests on the top of the end piece, with strong burrs, If 
inch square, to be turned by an iron spanner, made to 
fit them. 


OF SAW-MILLS. 


345 


These straps are made of flat bars, 3 feet 9 inches long, 
3 inches wide, three-fourths thick before turned; at the 
turn they are 5 inches wide, square, and split to receive 
the saw and lug pins, when brought near together, so as 
to fit the gate. The saw is stretched tightly in this frame, 
by the screws at the top; exactly in the middle, at each 
end, measuring from the outside; the top end standing 
about half an inch more forward than the bottom. 

Fig. 10—the forebay of water, projecting through the 
upper foundation wall. 

Fig. 11—the flutter wheel. Its diameter and length 
according to the head of water, as shown in the table. 
The floats are fastened in with keys, so that they will 
drive inward, when any thing gets under them, and not 
break. These wheels should be very heavy, that they 
may act as a fly, or balance, to regulate the motion, and 
work more powerfully. 

Fig. 12—the crank, (see it represented by a draught, 
from a scale of 1 foot to an inch, fig. IT, Plate XXIV.) 
The part in the shaft 2 feet 3 inches long, 3| by 2 inches, 
neck 8 inches long, 3 thick, and 12 inches from the cen¬ 
tre of the neck to the centre of the wrist or handle, 
which is 5 inches long to the key hole, and 2 inches 
thick. 

The gudgeon at the other end of the shaft is 18 inches 
in the shaft, neck 31 long, 21 diameter. 

The crank is fastened in the same way as gudgeons. 
(See Art. 132.) 

Fig. 12, 13—the pitman, which is 31 inches square 
at the upper end, 41 in the middle, and 4 near the lower 
end; but 20 inches of the lower end is 41 by 51, to hold 
the boxes and key, to keep the handle of the crank tight. 


Pitman Irons of an improved Construction. 

(See fig. 10, 11, 12, 13, 14, 18, Plate XXIV.) Fig. 
10 is a plate or bar, with a hole in each end, through 
which the upper ends of the lug-pins 11—11 pass, with 
a strong burr screwed on each; they are 17 inches long, 



OF S A W-M ILLS. 


346 


[chap. XXIII. 


18 inch square, turned at the lower end to make a round 
hole diameter; made strong round the hole. 

Fig. 12 is a large, flat link, through a mortise near 
the lower side of the end of the saw frame. The lug- 
pins pass one through each end of this link, which keeps 
them close to the gate sides. 

Fig. 14 is a bar of iron 2 feet long, 34 inches wide, 
one half inch thick at the lower, and 1| at the upper 
end. It is split at the top and turned as in the figure, 
to pass through the lug-pins. At fig. 13 there is a notch 
set in the head of the pitman bar 14, 14 inch long, nearly 
as deep as to be in a straight line with the lower side 
of the side-pins, made a little hollow, steeled and made 
very hard. 

Fig. 18 is an iron plate, 14 inch wide half an inch 
thick in the middle, with 2 large nail-holes in each end, 
and a round piece of steel welded across the middle and 
hardened, made to fit the notch in the upper end of the 
pitman, Plate XXVI., and draw close to the lug-pins, to 
the under side of the saw-frame, and nailed fast. Now, 
if the bearing part of this joint be in a straight line, the 
lower end of the pitman may play without friction in the 
joint, because both the upper and lower parts will roll 
without sliding, like the centre of a scale-beam, and will 
not wear. 

This is the best plan for pitman irons with which I am 
acquainted. The first set, so made, has been in my saw¬ 
mill 8 years, doing much hard work, and three minutes 
have not been required to adjust them. 

Fig. 14—the tub-wheel, for running the carriage back, 
This is a very light wheel, 4 feet diameter, and put in 
motion by means of the foot or hand, at once throwing it 
in gear with the rag-wheel, lifting off the hand and clicks 
from the ratchet, and hoisting a little gate to let water on 
the wheel. The moment the saw stops, the carriage 
begins to move gently back again with the log. 

Fig. 15—the cog-wheel on the top of the tub-wheel 
shaft, with 15 or 16 cogs. 

Fig. 16 — the log on the carriage, sawed partly 
through. 

Fig. 17—a crank and windlas, to increase power, by 



OF SAW-MILLS. 


347 


CHAP. XXIII.] 

which one man can draw heavy logs on the mill, and 
turn them, by a rope passing round the log and wind¬ 
lass. 

Fig. 18—a cant hook for rolling logs. 

Fig. 19—a double dog, fixed into the hindmost head- 
block, used by some to hold the log. 

Fig. 20—are smaller dogs to use occasionally at either 
end. 

Figs. 21, 22, represent the manner of shuting water on 
a flutter-wheel by a long, open sliute, which should not 
be nearer to a perpendicular than an angle of 45 de¬ 
grees, lest the water should rise from the sliute and take 
air, which would cause a great loss of power. 

Fig. 23 represents a long, perpendicular, tight sliute; 
the gate 23 is always drawn fully, and the quantity of 
water regulated at the bottom by a little gate r, for the 
purpose. There must be air let into this sliute by a 
tube entering at a. (See Art. 71.) These shutes are 
for saving expense where the head is great, and should 
be much larger at the upper than at the lower end, else 
there will be a loss of power. They must be very strong, 
otherwise they will burst. The perpendicular ones suit 
best where a race passes within twelve feet of the upper 
side of the mill. 

OPERATION. 

The sluice drawn from the penstock 10, puts the 
wheel 11 in motion—the crank 12 moves the saw-gate, 
and saw 9, up and down, and as they rise they lift up 
the lever 2, which pushes forward the liand-pole 3, 
which moves the rag-wheel 5, which gears in the cogs 
of the carriage 4, and draws forward the log 16 to meet 
the saw, as much as is proper to cut at a stroke. 
When it is within three inches of being through the log, 
the cleet C, on the side of the carriage, arrives at a trig¬ 
ger and lets it fly, and the sluice gate shuts down; the 
miller instantly draws water on the wheel 14, which 
runs the log gently back, &c. 


348 


OF A FULLING-MILL. 


[CHAP. XXIII. 


ARTICLE 159. 

DESCRIPTION OF A FULLING-MILL. 

Fig. 19, Plate XXIV., is the penstock, water-gate, and 
spoilt of an overshot fulling-mill, the whole laid down 
from a scale of 4 feet to an inch. 

Fig. 20—one of the three inter ties that are framed 
with one end into the front side of the top of the stock- 
block ; the other ends in the tops of the three circular 
pieces that guide the mallets; they are 6 feet long, 5 
inches wide, and 6 deep. 

Fig. 21—are two mallets: they are 4 feet 3 inches 
long, 21 inches wide, and 8 thick, shaped as in the figure. 

Fig. 22—their handles, 8 feet long, 20 inches wide, 
and three thick: a roller passes through them, 8 inches 
from the upper ends, and hangs in the liindermost cor¬ 
ner of the stock-post. The other ends go through the 
mallets, and have each, on their under-side, a plate of 
iron faced with steel and hardened, 2 feet long, 3 inches 
wide, fastened by screw-bolts, for the tappet-blocks to 
rub against while lifting the mallets. 

Fig. 23—the stock-post, 7 feet long, 2 feet square at 
the bottom, 15 inches thick at the top, and shaped as in 
the figure. 

Fig. 24—the stock where the cloth is beaten, shaped 
inside as in the figure, planked inside as high as the 
dotted line, which planks are put in rabbets in the post, 
the inside of the stock being 18 inches wide at the bot¬ 
tom, 19 at the top, and two feet deep. 

Fig. 25—one of the three circular guides for the mal¬ 
lets; they are 6 feet long, 7 inches deep, and 5 thick; 
are framed into a cross sill at bottom, that joints its 
lower edge to the stock-post. This sill forms a part of 
the bottom of the stock, and is 4 feet long, 20 inches 
wide, and 10 thick. 

The sill under the stock-post is G feet long, 20 inches 
wide, and 18 thick. The sill before the stock is 6 feet 
long, and 14 inches square. 

Fig. 26—the tappet-arms, 5 feet 6 inches long, 21 



CIIAP. XXIII.] OF A FULLING -MILL. 349 

inches each side of the shaft, 12 inches wide and 4 
thick. There is a mortise through each of them four 
inches wide, the length from shaft to tappet, for the 
ends of the mallet handles to pass through. The tap¬ 
pets are 4 pieces of hard wood, 12 inches long, 5 wide 
and 4 thick, made in the form of half circles pinned to 
the ends of the arms. 

Fig. 27 —an overshot water-wheel, similar to those in 
other mills. 

Fig. 28—one of the 3 sills, 16 feet long, and 16 inches 
square, with walls under them, as in the figure. 

OPERATION. 

The cloth is put in a loose heap in the stock 24; the 
water being drawn on the wheel, the tappet-arms lift 
the mallets, alternately, which strike the under part of 
the heap of cloth, and the upper part is continually fall¬ 
ing over, and thereby turning and changing its position 
under the mallets, which are shaped as in the figure, to 
produce this effect. 

Descr iption of the drawings of the iron-work , Plate XXI V. 

Fig. 1 is a spindle, 2 the balance ryne, and 3 the dri¬ 
ver, for a mill-stone. The length of the spindle from 
the foot to the top of the neck is about 5 feet 3 inches; 
cock-head 8 or 9 inches from the top of the neck, which 
is 3 inches long and 3 diameter; blade or body 3i by 2 
inches; foot one and a quarter inches diameter; the 
neck, foot and top of the cock-head, steeled, turned and 
hardened. 

Fig. 2—the balance-ryne is sometimes made with 3 
horns, one of which is so short as only to reach to the 
top of the driver, which is let into the stone directly un¬ 
der it; the other to reach nearly as low as the bottom 
of the driver: of late, they are mostly made with two 
horns only: this may be made sufficiently fast by making 
it a little wider than the eye, and letting it into the 
stone a little on each side, to keep it steady and pre¬ 
vent its moving sidewise. Some choose them with four 
horns, which fill the eye too much. 


350 


OF SAW-MILLS. 


[cnAP. XXIII. 

Fig. 3—is a driver, about 15 inches long. 

Fig. 4—the step for the spindle foot to run in. It is 
a box G inches long, 4 inches wide at the top, but less 
at bottom, and 4 inches deep outside, at the sides and 
bottom half an inch thick. A piece of iron 1 inch thick 
is fitted to lie tightly in the bottom of this box, but not 
welded: in the middle of this is welded a plug of steel 
one and a half inches square, in which is punched a hole 
a quarter of an inch deep, to fit the spindle foot. The 
box must be tight, to hold oil. 

Fig. 5—a step-gudgeon for large upright shafts, 1G 
inches long, and 2 square, steeled and turned at the toe. 

Fig. G—the step for it, similar to 4, but proportion¬ 
ally less. 

Fig. 7—a gudgeon for large bolting-shafts, 13 inches 
long, and one and a half square. 

Fig. 8—a large joint-gudgeon, tang 14 inches, neck 
5, and tenon 2 inches long, one and a half square. 

Fig. 9—the socket part to fit the shaft, with three 
rivet-holes in each. 

Fig. 10, 14, 18—pitman irons, described Art. 158. 

Fig. 15—the wallower gudgeon, tang 16 inches, neck 
31 inches long, and 21 diameter. 

Fig. 1G—the water-wheel gudgeon, tang 3 feet 2 
inches long, neck 41 inches long, 31 square. 

Fig. 17—a saw-mill crank, described Art. 158. 

N. B.—The spindle-ryne, &c., is drawn from a scale 
of two feet to an inch, and all the other irons one foot 
to an inch. 


ARTICLE 160. 

To what has been said of saw-mills, by Thomas Elli- 
cott, I add the following:— 

Of hanging the saw. 

First, set the fender posts as nearly plumb every way 
as possible, and the head-blocks on which the log is to 
lie level. Put the saw just in the middle of the gate. 





CHAP. XXIII.J OF SAW-MILLS. 351 

measuring from the outsides, set it by the gate and not 
by a plumb line, with the upper teeth about half an inch 
farther forward than the lower ones:—this is to give the 
saw liberty to rise without cutting, and the log room to 
push forward as it rises. Run the carriage forward so 
that the saw may strike the block—strike up a nail, &c., 
there: run it back again its full length, and standing be¬ 
hind the saw, set it to direct exactly to the mark. Stretch 
the saw in the frame, rather the most at the edge, that it 
may be stiffest there. Set it in motion, and hold a tool 
close to one side of it, and observe whether it touch equal 
the whole length of the stroke—try if it be square with 
the top of the head-blocks, else it will not make the scant¬ 
ling square. 

Of Whetting the Saw. 

The edge of the teeth ought to be kept straight, and 
not suffered to wear hollowing—set the teeth a little out 
equal at each side, and the outer corners a little longest ; 
they will then clear their way. Some whet the under 
side of the teeth nearly level, and others a little droop¬ 
ing down, but it then never saws steadily, but is apt to 
wood too much; the teeth should slope up, although but 
very little. Try a cut through the log, and if it come 
out at the mark made to set it by, it is shown to be 
hung right. 

Of springing logs straight. 

Some long small logs will spring so much in sawing, 
as to spoil the scantling, unless they can be held straight; 
to do which make a clamp to bear with one end against 
the side of the carriage, the other end under the log, 
with a post up the side thereof—drive a wedge between 
the post and log, and spring it straight; this will bend 
the carriage side, but this is no injury. 


Of moving the logs to the size of the scantling , &c. 

Make a sliding block to slide in a rabbet in front of 
the main head-block; fasten the log to this with a little 
dog on each side, one end of which being round, is driven 
into a round hole, in the front side of the sliding-block. 


OF SAW-MILLS. 


352 


[chap. XXIII. 


tlie other flattened to drive in the log, cutting across the 
grain, slanting a little out—it will draw the log tight 
and stick in it the better. Set a post of hard wood in 
the middle of the main block, close to the sliding one, 
and to extend with a shoulder over the sliding one, for 
a wedge to be driven under this shoulder to keep the 
block tight. Make a mark on each block to measure 
from—when the log is moved the key is driven out. 
The other end next the saw is best held by a sliding 
dog, part on each side of the saw, pointed like a gouge, 
with two joint dogs, one on each side of the saw. 


Remedy for a long pitman. 

Make it in two parts by a joint 10 feet from the 
crank, and a mortise through a fixed beam, for the lower 
end of the upper part to play in; the gate will work 
more steadily, and all may be made lighter. 

The feed of a saw-mill ought to be regulated by a 
screw fixed to move the liand-pole nearer or farther 
from the centre of the roller that moves it, which may 
be done, as the saw arrives at a knot, without stopping 
the mill. 


ARTICLE 161. 

The folloiving observations on Saw-Mills , ef'e., were communi¬ 
cated by William French , mill-wright , New Jersey. 

Saw mills, with low heads, have been much improved 
in this state. Mills with two saws, with not more than 
7 feet head and fall, have sawed from five to six hundred 
thousand feet of boards, plank and scantling, in one year. 
If the water be put on the wheel in a proper manner, 
and the wheel of a proper size, (as by the following ta¬ 
ble,) the saw will strike between 100 and 130 strokes in 
a minute, (see fig. 1, Plate XXVI.) The lower edge of 
the breast-beam B to be three fourths the height of the 
wheel, and one inch to a foot, slanting up stream, fast¬ 
ened to the penstock posts with screw-bolts, (see post A) 



OF SAW-MILLS. 


353 


CHAP. XXIII.] 

circled out to suit the wheel C; the fall D circled to suit 
the wheel, and extending to F, two inches above the 
lower edge of the breast-beam, or higher, according to 
the size of the throat or sluice E, with a shuttle, or gate, 
sliding on F E, shutting against the breast-beam B: 
then 4 buckets out of 9 will be acted on by the water. 
The method of fastening the buckets or floats is, to step 
them in starts mortised in the shaft—see start G—9 
buckets in a wheel 4£ inches wide, see them numbered 
1, 2, &c. 

Fig. 2, the go back, is a tub wheel. Its common size 
is from 41 to 6 feet diameter, with 16 buckets. The 
water is brought on it by the trunk H. The bucket 1. 
is made with a long tenon, so as to fasten it with a pin 
at the top of the wheel. 

TABLE 

Of the Dimensions of Flutter-wheels. 


Head 12 feet. 

Bucket 5 feet. 

Wheel 3 feet. 

Throat 1| inches. 

11 


3 

2 

10 

6 

3 

ol 

2? 

9 

6| 

2 10 inches. 

8 

r* 

i 

2 9 


7 


2 8 

H 

G 

8 

2 7 p. 

H 

5 

9 

2 6 



N. B.—The crank about 11 inches, but varies to suit the timber. 

The Pile Engine. 

Fig. 3, a simple machine for driving piles in soft bot¬ 
toms for setting mill walls or dams on. It consists of a 
frame 6 or 7 feet square, of scantling, 4 by 5 inches, with 

2 upright posts 2 inches apart, 10 or 12 feet high, 3 by 

3 inches, brace from top to bottom of the frame, with a 
cap on top 2 feet long, 6 by 8 inches, with a pulley in 
its middle, for a rope to bend over, fastened to a block 
I, called a tup, which has 2 pieces, 4 inches wide be¬ 
tween the uprights, with a piece of 2 inch plank T, 6 
inches wide, framed on the ends, so as to slide up and 
down the upright posts S. This machine is worked by 

4 or 6 men, who draw the tup up by the sticks fastened 
to the end of the rope K, and let it fall on the pile L; 
they can thus strike 30 or 40 strokes in a minute by 
the swing of their arms. 

23 


354 


OF SAW-MILLS. 


[CIIAP. XXIII. 


Of building Dams on soft foundations. 

The best method is to lay three sills across the stream, 
and frame cross sills into them up and down stream, 
setting the main mud sills on round piles, and pile them 
with two-inch plank, well jointed and driven closely 
together, edge to edge, from one end to the other. 
Taking one corner off the lower end of the plank will 
cause it to keep a close joint at bottom, and by driving 
an iron dog in the mud-sill, and a wooden wedge to' 
keep it close at the top end, it will be held to its place 
when the tup strikes. It is necessary to pile the out¬ 
side cross sills also in some bottoms, and to- have wings 
to run 10 or 12 feet into the bank at each side; and the 
wing posts two or three feet higher than the posts of 
the dam, where the water falls over, planked to the top 
N N, and filled with dirt to the plate 0. 

Fig. 4 is a front view of the breast of the tumbling 
dam. 

Fig. 5 is a side view of the frame of the tumbling dam, 
on its piling a, b, c, d, e, and f, g, h is the end of the 
mud-sills. The posts k are framed into the main mud¬ 
sills with a hook tenon, leaning down stream 6 inches 
in 7 feet, supported by the braces 11, framed into the 
cross-sills I; the cross sills I to run 25 feet up and down 
stream, and to be well planked over, and the breast- 
posts to be planked to the top, (see P, fig. 4,) and filled 
with dirt on the upper side, within 12 or 18 inches of 
the plate 0, (see Q, fig. 5) slanting to cover the up¬ 
stream ends of the sills 3 or 4 feet deep. R represents 
the water. 

When the heads are high, it is best to plank the 
braces for the water to run down; but, if low, it may 
fall perpendicularly on the sheeting. 


CHAP. XXIV.] 


PATH TO INVENTIONS. 


355 


CHAPTER XXIV. 

RULES FOR DISCOVERING NEW IMPROVEMENTS; EXEMPLIFIED IN 

IMPROVING THE ART OF CLEANING AND HULLING RICE, WARM¬ 
ING ROOMS, VENTING SMOKE BY CHIMNEYS, ETC.* 

The True Path to Inventions. 

Necessity is called the mother of invention, but, 
upon inquiry, we shall find that Reason and Experi¬ 
ment bring it forth; for almost all inventions have re¬ 
sulted from such steps as the following:— 

I. To investigate the fundamental principles of the 
theory, and process of the art, or manufacture, we wish 
to improve. 

II. To consider what is the best plan, in theory, that 
can be deduced from, or founded on, those principles, 
to produce the effect we desire. 

III. To inquire whether the theory be already put in 
practice to the best advantage; and what are the im¬ 
perfections or disadvantages of the common process, and 
what plans are likely to succeed better. 

IV. . To make experiments in practice, upon any plans 
that these speculative reasonings may suggest or lead 
to. Any ingenious artist, taking the foregoing steps, 
will probably be led to improvement on his own art; 
for we see by daily experience, that every art may be 
improved. It will, however, be in vain to attempt im¬ 
provements, unless the mind be freed from prejudices 
in favour of established plans. 

EXAMPLE I. 

On the Art of Gleaning Grain by Wind. 

1. What are the principles on which the art is found¬ 
ed ? When bodies fall through resisting mediums, their 

* The rules and observations which formed an appendix to the former editions 
of this w’ork, contain some suggestions which are worthy of attention. Since 
they were written many improvements have been made in the processes to 
which they refer; but the path is still open, and perhaps the remarks made by 
Mr. Evans may yet lead to useful results; with this hope they have, with some 
modifications, been retained. 


356 


PATH TO INVENTIONS. [CIIAP. XXIV. 

velocities are as their specific gravities, and the surface 
they expose to the medium; consequently, when light 
and heavy articles are mixed together, the farther they 
fall, the greater will be their distance apart; on this 
principle a separation can be effected. 

II. What is the best plan in theory? First, make a 
current of air as deep as possible, for the grain to fall 
through; the lightest will then be carried farthest, and 
the separation be more complete at the end of the fall. 
Secondly, cause the grain, with the chaff, &c., to fall in 
a narrow line across the current, that the light parts 
may meet no obstruction from the heavy in being car¬ 
ried forward. Thirdly, fix a moveable board edgewise 
to separate between the good clean, and the light grain, 
&c. Fourthly, cause the same blast to blow the grain 
several times, and thereby effect a complete separation 
at one operation. 

III. Is this theory in practice already ? What are 
the disadvantages of the common process? We find 
that the farmers’ common fans drop the grain in a line 
15 inches wide, to fall through a current of air about 8 
inches deep, instead of falling in a line half an inch 
wide, through a current three feet deep; so that it re¬ 
quires a very strong blast even to blow out the chaff; but 
garlic, like grains, &c., cannot be thus removed, as they 
meet so much obstruction from the heavy grains; the 
grain has, therefore, to undergo two or three such ope¬ 
rations, so that the practice appears absurd, when tried 
by the scale of reason. 

IY. The fourth step is to construct a fan to put the 
theory in practice, by experiment. (See Art. 83.) 

EXAMPLE II. 

The Art of Distillation . 

I. The principles on which this art is founded, are 
evaporation and condensation. When liquid is heated, 
the spirit it contains, being more volatile than the wa¬ 
tery part, evaporates, before it, into steam, which being 
condensed again into a liquid, by cold, is obtained in a 
separate state. 


357 


CHAP. XXIV.] PATH TO INVENTIONS. 

II. The best plan, in theory, for effecting this, ap¬ 
pears to be as follows: the fire should be applied to the 
still, so as to spend the greatest possible part of its heat 
to heat the liquid. Secondly, the steam should be 
conveyed into a metallic vessel of any suitable form, 
and this should be immersed in cold water, to condense 
the steam: in order to keep the condenser cold, there 
should be a stream of cold water continually entering 
the bottom and flowing over the top of the condensing 
tub; the steam should have no free passage out of the 
condenser, else the strongest part of the liquor will escape. 

III. Is this theory already put in practice, and what 
are the disadvantages of the common process?—1st, A 
great part of the heat escapes up the chimney. 2dly, 
It is almost impossible to keep the grounds from burning 
in the still. 3dly, The fire cannot be regulated to keep 
the still from boiling over; we are, therefore, obliged to 
run the spirit off very slowly; how are we to remedy 
these disadvantages ?—First, to lessen the fuel, apply the 
fire as much to the surface of the still as possible; enclose 
the fire by a wall of clay that will not convey the heat 
away so fast as stone; let in no more air than is necessary 
to keep the fire burning, for the surplus air carries away 
the heat of the fire. Secondly, to keep the grounds from 
burning, immerse the still, with the contained liquor, 
in a vessel of water, joining their tops together; then, 
by applying the fire to heat the water in the outside 
vessel, the grounds will not burn, and by regulating the 
heat of the outside vessel the still may be kept from boil¬ 
ing over. 

IV. A still to be heated through the medium of water, 
was made, some years ago, by Colonel Alexander Ander¬ 
son, of Philadelphia, and the experiment tried; but the 
outside vessel being open, the water in it boiled away, 
and carried off the heat, and the liquor in the still could 
not be made to boil—this appeared to defeat the scheme. 
But, by enclosing the water in a tight vessel, so that the 
steam could not escape, and that the heat might be in¬ 
creased, it now passed to the liquor in the still, which 
boiled as well as if the fire had been immediately applied 
to it. By fixing a valve to be loaded so as to let the 


858 


PATH TO INVENTIONS. [CHAP. XXIV. 

steam escape, when it has arrived at such a degree of 
heat as to require it, all danger of explosion is avoided, 
and all boiling over prevented. 

EXAMPLE III. 

t 

The Art of venting Smoke from Rooms by Chimneys. 

I. The principles are:—Heat, by repelling the parti¬ 
cles of air to a greater distance than when cold, renders 
it lighter than cold air, and it will rise above it, forming 
a current upwards, with a velocity proportional to the 
degree of heat, and the size of the tube or funnel of the 
chimney, through which it ascends, and with a power 
proportional to its perpendicular height: which power 
to ascend will always be equal to the difference of the 
weight of a column of rarefied air of the size of the small¬ 
est part of the chimney, and a column of common air of 
equal size. 

II. What is the best plan, in theory, for venting 
smoke, that can be founded on these principles ? 

1st. The size of the chimney must be proportioned to 
the size and closeness of the room and to the fire; be¬ 
cause, if the chimney be immensely large,*and the fire 
small, there will be little current upwards. And, again, 
if the fire be large, and the chimney too small, the smoke 
cannot be all vented by it: more air being necessary to 
supply the fire, than can find vent up the chimney, it 
must spread in the room again, which air, after passing 
through the fire, is rendered deleterious. 

2dly. The narrowest place in the chimney must be 
next the fire, and in front of it, so that the smoke would 
have to pass under it to get into the room ; the current 
will there be greatest, and will draw up the smoke 
briskly. 

3dly. The chimney must be perfectly tight, so as to 
admit no air but at the bottom. 

III. The errors in chimneys in common practice, are, 

1st. In making them widest at bottom. 

2dly. Too large for the size and closeness of the room. 

odly. In not building them high enough, so that the 
wind, whirling over the tops of houses, blows down them. 


CHAP. IXXIV.] PATH TO INVENTIONS. 359 

4tilly. By letting in air any where above the breast 
or opening, which destroys the current of it at the bot¬ 
tom. 

IV. The cures directed by the principles and theory, 
are, 

1st. If the chimney smoke on account of being too 
large for the size and closeness of the room, make the 
chimney less at the bottom—its size at the top may not 
do much injury, but it will weaken the power of ascent, 
by giving the smoke time to cool before it leave the chim¬ 
ney ; the room may be as tight, and the fire as small as 
you please, if the chimney be in proportion. 

2dly. If it be small at the top and large at the bottom, 
there is no cure but to lessen it at the bottom. 

odly. If it be too small, which is seldom t he case, stop 
up the chimney and use a stove—it will be large enough 
to vent all the air that can pass through a two-inch hole, 
which is large enough to sustain the fire in a stove. 
Chimneys built in accordance with these theories, I be¬ 
lieve, are every where found to answer the purpose. 
(See Franklin s letters on smoky chimneys.) 

EXAMPLE IV. 

The Art of Warming Booms by Fire. 

I. Consider in what way fire operates. 

1st. The fire heats and rarefies the air in the room, 
which gives us the sensation of heat or warmth. 

2dly. The warmest part of the air being lightest, rises 
to the uppermost part of the room, and will ascend 
through holes (if there be any) to the room above, making 
it warmer than the one in which the fire is. 

3dly. If the chimney be too open, the warm air will 
tly up it, leaving the room empty; the cold air will then 
rush in at all crevices to supply its place, which keeps 
the room cold. 

II. Considering these principles, what is the best plan 
in theory for warming rooms ? 

1st. We must contrive to apply the fire to spend all 
its heat, to warm the air which comes into the room. 


3G0 PATH TO INVENTIONS. [CHAP. XXIV. 

2dly. The warm air must be retained in the room as 
long as possible. 

odly. Make the fire in a lower room, conducting the 
heat through the floor into the upper one, and leaving 
another hole for the cold air to descend to the lower 
room. 

4thly. Make the room so tight as to admit no more 
cold air than can be warmed as it comes in. 

5thly. By closing the chimney so as to let no warm air 
escape, but that which is absolutely necessary to sustain 
the fire—a hole of two square inches will be sufficient 
for a very large room. 

Gthly. The fire may be supplied by a current of air 
brought from without, not using any of the air already 
warmed. If this theory, which 1 is founded on true princi¬ 
ples and reason, be compared with common practice, the 
errors will appear, and may be avoided. 

I had a stove, constructed in accordance with these 
principles, and have found all to answer according to 
theory. 

The operation and effects are as follows, namely:— 

1st. It applies the fire to warm the air as it enters the 
room, and admits a full and fresh supply, rendering the 
room moderately warm throughout. 

2dly. It effectually prevents the cold air from pressing 
in at the chinks or crevices, but causes a small current 
to pass outward. 

3dly. It conveys the coldest air out of the room first, 
consequently, 

4thly. It is a complete ventilator, thereby rendering 
the room healthy. 

Gthly. The fire maybe supplied (in very cold weather) 
by a current of air from without, that does not communi¬ 
cate with the warm air in the room. 

Gthly. Warm air may be retained in the room any 
length of time, at pleasure; circulating through the stove 
the coldest entering first, to be warmed over again. 

Tthly. It will bake, roast, and boil equally well with 
the common ten-plate stove, as it has a capacious oven. 

Stilly. In consequence of these improvements, it re¬ 
quires not more than half the usual quantity of fuel. 


CHAP. XXIV.] 


PATH TO INVENTIONS. 


361 


Description of the Philosophical and Ventilating Stove. 

It consists of three parts, either cylindrical or square, 
the greatest surrounding the least. (See fig. 1, Plate 
X.) S F is a perspective view thereof in a square form, 
supposed open at one side: the fire is put in at F, into 
the least part, which communicates with the space next 
the outside, where the smoke passes to the pipe 1—5. 
The middle part is about two inches less than the out¬ 
side part, leaving a large space between it, and above 
the inner part, for an oven in which the air is warmed, 
being brought in by a pipe B D between the joists of 
the floor, from a hole in the wall at B, it rises under the 
stove at D, into the space surrounding the oven and the 
fire, which air is again surrounded by the smoke flue, 
giving the fire a full action to warm it, whence it ascends 
into the room by the pipe 2. E brings air from the pipe 
D B to blow the fire. FI is a view of the front end plate, 
showing the fire and oven doors. I is a view of the back 
end, the plate being off, the dark square shows the space 
for the fire, and the light part the air-space surrounding 
the fire, the dark outside space the smoke surrounding 
the air; these are drawn on a larger scale. The stove 
consists of fifteen plates, twelve of which join, by one 
end, against the front plate H. 

To apply this stove to the best advantage, suppose 
fig. 1, Plate X., to represent a three or four-story house, 
two rooms on a floor—set the stove S F in the partition 
on the lower floor, half in each room; pass the smoke pipe 
through all the stories; make the room very close; let no 
air enter but what comes in by the pipes A B or G C 
through the wall at A and G, that it may be the more 
pure, and pass through the stove and be warmed. But 
to convey it to any room, and take as much heat as pos¬ 
sible with it, there must be an air-pipe surrounding the 
smoke pipe, with a valve to open at every floor. Sup¬ 
pose we wish to warm the rooms No. 3—6, we open the 
valves, and the warm air enters, ascends to the upper 
part, depresses the cold air, and if we open the holes a—c, 
it will descend the pipes, and enter the stove to be 
warmed again: this may be done in very cold weather. 


362 


PATH TO. INVENTIONS. [CIIAP. XXIV. 

The higher the room above the stove, the more power¬ 
fully will the warm air ascend and expel the cold air. 
But if the room require to be ventilated, the air must be 
prevented from descending, by shutting the little gate 
2 or 5, and drawing 1 or 6, and giving it liberty to as¬ 
cend and escape at A or G—or up the chimney, letting 
it in close at the hearth. If the warm air be conveyed 
under the floor, as between 5—6, and let rise in several 
places, with a valve at each, it will be extremely conve¬ 
nient and pleasant; if above the floor, as at 4, several 
persons might set their feet on it to warm. The rooms 
will be moderately warm throughout—a person will not 
be sensible of the coldness of the weather. 

One large stove of this construction may be made to 
warm a whole house, ventilate the rooms at pleasure, 
bake bread, meat, &c. 

These principles and improvements ought to be con¬ 
sidered and provided for in building. 

EXAMPLE Y. 

Art of Hulling and Cleaning Rice. 

\ i 

Step I. The principles on which this art may be 
founded, will appear, by taking a handful of rough rice, 
and rubbing it hard between the hands—the hulls will 
be broken off, and, by continuing the operation, the 
sharp texture of the outside of the hull (which, through 
a magnifying glass, appears like a sharp, fine file, and 
no doubt is designed by nature for the purpose) will 
cut off the inside hull, and the chaff being blown out, 
will leave the rice perfectly clean, without breaking any 
of the grains. 

II. What is the best plan in theory for effecting this ? 
(See the plan proposed, represented in Plate X., fig. 2; 
explained Art. 103.) 


CHAP. XAIV. J PATH TO INVENTIONS. 



EXAMPLE YI. 

To save Ships from Sinking at Sea. 

Step I. The principle on which ships float, is the 
difference of their specific gravities from that of the wa¬ 
ter—sinking only to displace a quantity of water equal 
in weight to that of the ship and its lading; they sink 
deeper, therefore, in fresh than in salt water. If we can 
calculate the weight of the cubic feet of water a ship dis¬ 
places when empty, it will show her weight, and sub¬ 
tracting that from what she displaces when loaded, shows 
the weight of her load; each cubic foot of fresh water 
weighing 62.5 lbs. If an empty rum hogshead weigh 
62.5 lbs, and measure 15 cubic feet, it will require 875 
lbs. to sink it. A vessel of iron, containing air only, and 
so large as to make its whole bulk lighter than so much 
water, will float, but if it be filled with water, it will 
sink. Hence, we may conclude, that a ship loaded with 
any thing that will float, will not sink if filled with 
water; but if loaded with any thing specifically heavier 
than water, it will sink as soon as filled. 

II. This appears to be the true theory;—How is it to 
be applied, in case a ship spring a leak, that gains on 
the pumps? 

III. The mariner who understands well the above 
principles and theory will be led to the following steps: 

1st. To cast overboard such things as will not float, 
and carefully to reserve every thing that will float, for 
by them the ship may at last be buoyed up. 

2dly. To empty every cask or thing that can be made 
water-tight, to put them in the hold, and fasten them 
down under the water, filling the vacancies between them 
with billets of wood; even the spars and masts may, in des¬ 
perate cases, be cut up for this purpose, which will fill 
the hold with light matter, and as soon as the water in¬ 
side is level with that outside no more will enter. If 
every hogshead buoy up 875 lbs., they will be a great 
help to buoy up the ship, (but care must be taken not to 
put the empty casks too low, which would overset the 
ship,) and she will float, although half the bottom be 


3G4 


PATH TO INVENTIONS. [CHAP. XXIV. 

torn off. Mariners, for want of this knowledge, often 
leave their ships too soon, taking to their boats, although 
the ship be much the safest, and do not sink lor a long 
time after being abandoned—not considering that, al¬ 
though the water gain on their pumps at lirst, they may 
be able to hold way with it when risen to a certain height 
in the hold, because the Velocity with which it will enter, 
will be in proportion to th4-£quare root of tlie difference 
between the level of the water inside and outside-—added 
to this, the fullefc* the ship the easier the pumps Will work, 
because the watct has to be raised to a less height; there¬ 
fore, they ought not to be^too soon discouraged. 



Description of the Thrashing Machine , with Elastic Flails ; 
invented by James Wardrop, of Ampthill, Virginia* 


plate xxv. 


A—The floor on which the flails are 
fixed. 

B—The part of the floor on which the 
grain is laid, made of wicker-work, 
through which the grain fall s, and is 
conveyed to the fan or>eT€eh oelow - 
the pivot of the faHr't&'Seen 
is turned by a b and from the"\vTieel, 
or wallower. 


I I I—Catchers or teeth to raise the 
lifters. 

K—Post on which the wallower is fixed. 
L—Beam on which the lifters rest and 
fixed by an iron rod passing 
lifters, and let into this 


are 

thi 


the 


tm. 


raised round the 
the wheat, and made 
rds, to render raking 
e easy. 
whe< 


C C C—A thin 
floor to confi 
shelving out 
off the straw 
D—The wallovve 
E—Crank handle to 
F F—Flails. 

G G G—Lifters, with ropes fixed to the 
flails. 


ilMRb 


__ to stop the end of the 

lifters ’fforp rising. 

N—Keeps in*whieh the lifters work. 

O—Beam in which the ends of the flails 
are mortised. 

Fly-ends loafed with lead, not ne¬ 
cessary irp^fiorse machine. 

R—Showing the lifters and keeps, how 


The machine, to be worked by two men, was made on a scale of a 12 feet 
flail, having a spring which required a power of 20 lbs. to laise it three feet high 
at the point;—A spring of this power, and raised three feet high, being found 
to get out wheat with great effect. 


* The flail thrashing machine has been superseded by .that with cylindrical 
beaters, and a concave, variously modified. This is now so generally introduced 
as not to require any description. The flail machine having been originally 
engraved for this work, has been retained. 









appendix; 

CONTAINING 

A DESCRIPTION OF A MERCHANT FLOUR MILL ON THE MOST 
APPROVED CONSTRUCTION, WITH THE RECENT IMPROVE¬ 
MENTS, WITH TWO ADDITIONAL PLATES. 

*v 

BY CADWALLADER AND OLIVER EVANS, ENGINEERS. 

« 

AND 

EXTRACTS 

FROM SOME OF THE BEST MODERN WORKS ON THE SUBJECT OF MILLS. 

WITH OBSERVATIONS BY THE EDITOR. 

Description of a Merchant Flour Mill, driving four pairs of 
five feet mill-stones; arranged by Cadwallader and Oliver 
Evans , Engineers , Philadelphia. 

PLATE XXVII. 

1— A hollow cast-iron shaft, circular, 15 inches in dia¬ 
meter except at those points where the water and 
main bevel-wheels are hung, where it is increased to 
19 inches in diameter. The water-wheel is secured 
on this shaft by 3 sockets, as represented in Plate 
XXVIII., lig. 3, and makes 10 revolutions per minute. 

2— The main driving bevel-wheel, on the water-wheel 
shaft, 8 feet in diameter, to the pitch line; 100 cogs, 
3 inches pitch, and 8 inches on the face, revolving 10 
times per minute, and driving 

3— A bevel-wheel on the upright, 4 feet in diameter to 
pitch line; 50 cogs, same pitch and face of cogs as 
above, revolving 20 times per minute. 

4— The large pit spur-wheel, making 20 revolutions per 
minute, 9 feet jth inch diameter, to pitch line; 114 cogs, 



366 


APPENDIX. 


3 inches pitch, face 10 inches: this wheel gives mo¬ 
tion to 

5, 5, 5, 5—Four pinions on the spindles of the mill¬ 
stones, 18.1 inches in diameter to pitch line, 19 cogs, 
same face and pitch. 

6, 6, 6, 6—Iron upright shafts, extending the height ot 
the building, and coupled at each story. 

7, 7, 7, 7—Are four pairs of five feet mill-stones, making 
120 revolutions per minute. Two of them shown in 
elevation; and the position of the 4, shown in Plate 
XXVIII., as represented by the dotted lines, fig. 1. 

8—A pulley on the upright shaft, which, by a band, 
gives motion to 

8— The fan for cleaning grain, revolving 140 times per 
minute, wings 3 feet long, 20 inches in width. 

9— A bevel-wheel 2 feet diameter, cogs 2 inches pitch, 
face 2.5 inches on the upright shaft, gearing into a 
bevel-wheel, the face of which is shown, drives the 
bolting screen 18 revolutions per minute. 

10— A bevel-wheel on upright shaft, 56 cogs 2 inches 
pitch, 2.5 inches face, gearing into 

10— A bevel-wheel on the shaft of the bolting reels, 31 
cogs, same pitch and face. 

10, 10—Are two of four bolting reels shown, 18 feet 
long, 30 inches diameter, revolving 36 times per mi¬ 
nute. 

11— A large pulley on the upright shaft, which, by a 
band, gives motion to the rubbing stones 11. 

12— A bevel-wheel on the top of the upright shaft 
gearing into 

O O 

12— A bevel-wheel, on the horizontal shaft, at one‘end 
of which is 

13— A bevel-wheel, one foot diameter, gearing into a 
bevel-wheel 

14— Of 5 feet diameter, which reduces the motion of the 
hopper-boy down to 4 revolutions per minute, which 
sweeps a circle of 20 feet. 

15— Meal elevator attending 4 pairs of stones. 

16— Grain elevator. 

1 7—Packing-room and press. 



APPENDIX. 


367 


PLATE XXVIII. 

Figure 1. 

A bird’s-eye view of the mode of giving motion to four 
pairs of mill-stones. 

4—The large pit spur-wheel, driving, at equal distances 
on its periphery, the pinions. 

5, 5, 5, 5—Attached to the spindles of the mill-stones. 

7, 7, 7, 7—Mill-stones 5 feet diameter, represented by 
dotted circles. 

Figure 2. 

An enlarged view of the couplings of the upright shaft. 
They are of cast-iron, with their holes truly reamed, 
to receive the ends of the iron upright shafts. 

2—The face of a coupling divided into six equal parts, 
radiating from the centre: three of the parts project, 
and three are depressed, so that when two of them 
are coupled, the projections of one will till the de¬ 
pressions in the other, as 1, the coupling connected. 

Figure 3. 

A cast-iron socket for the water-wheel; it is a plate 
three-fourths of an inch thick; the eye for the shaft 
to pass through one and a quarter inches thick, and 
12 inches deep; the sockets, for receiving the arms, 
are 14 inches long, and have projections 5 inches 
deep: 3, 3, 3,&c., are the projections; the intermedi¬ 
ate space between the sockets, are cut out to lessen 
the weight of metal, but in such a manner as to pre¬ 
serve the •strength. It requires three of these sockets 
for a large water-wheel; the arms for receiving the 
buckets are dressed to fit tightly in the sockets; and 
secured firmly by bolts, as 2, 2. 

Figure 4. 

Is an arm for the water-wheel, as dressed; 1, the end 
to be bolted in the socket; 2, the end for screwing on 
the bucket. 

The advantages of this mode of constructing water- 



368 


APPENDIX. 


wheels is, that the shaft is not weakened, by having 
mortises cut in to receive the arm; that it is not so li¬ 
able to decay, and if an arm or bucket be destroyed by 
accident, they can be dressed out, and the mill stopped, 
only while you unscrew the broken part, and replace it 
by a new one. 

Figure 5 , 

An elevation of the flour press. 1, the barrel of flour; 
2, the funnel; 3 3, the driver; 4 5, the lever; 4 3, the 
connecting bars, fastened by a strong pin to each 
side of the lever at 4, and to the driver at 3. 6, a 

strong bolt, passing through the floor, and keyed be¬ 
low the joist; there is a hole in the upper part of the 
bolt, to receive a pin which the lever works on, which, 
when brought down by the hand, moves the pin 4, 
in the dotted circle; the connecting bars drawing 
down the driver 3 3, pressing the flour into the bar¬ 
rel; and as it becomes harder packed, the power of 
the machine increases; as the pin 4 approaches the 
bolt 6, the under-sliding part of the lever is drawn 
out, to increase its length; and is assisted in raising 
by a weight fastened to a line passing over pulleys. 

When the pin 4 is brought down within half an inch 
of the centre of the bolt 6, or plumb line, the power in¬ 
creases from 1 to 288; and with the aid of a simple wheel 
and axis, as 1 to 15, from 288 to 4320; or, if the wheel 
and axis be as 1 to 30, it will be increased to 4320; that 
is to say, one man will press as hard with this machine 
as 8640 men could do with their natural strength. It 
is extremely well calculated for cotton, tobacco, cider, 
or, in short, any thing that requires a powerful press. 

Operation of the mill:—The grain, after having been 
weighed, by drawing a slide, is let into the grain eleva¬ 
tor 16, then hoisted to the top of the building, and, by 
a spout moving on a circle, can be deposited into spouts 
leading to any part of the mill, when wanted for use: 
by drawing sliders in other spouts, converging to the 
grain elevator 16, it can be re-elevated, and thrown 
into the hopper of the rubbing stones 11; after passing 
through which it descends into the bolting screen 9, and 


APPENDIX. 


369 


when screened, falls into the fan 8, is there cleaned, and 
from that descends into a very large hopper, over the 
centre of the four pairs of mill-stones, which are sup¬ 
plied regularly with grain. After being ground, the 
meal descends into a chest, is taken by the elevator 15, 
to the top of the building, there deposited under the 
hopper-boy, which spreads, cools, and collects it to the 
bolting reels, where the several qualities are separated, 
and the flour descends into the packing room 17, where 
it is packed in barrels. 

By this arrangement, we dispense with all conveyers, 
and have only one grain, and one flour-elevator, to at¬ 
tend two pairs of stones; we also dispense with one-half 
the quantity of gearing usually put into mills, and con¬ 
sequently occupy much less space, leaving the rest of 
the building for stowing grain, &c. 

All the wheels in this mill are. of cast-iron, and the 
face of the cogs very deep; for experience justifies 
the assertion that depth of face in cog-wheels, when 
properly constructed, does not increase friction; and 
that the wheels will last treble the time, by a small 
increase of depth: we recommend the main driving 
wheels to be 10 inches on tli.e face. The journals of 
all shafts, when great pressure is applied, should be of 
double the length now generally used: increase of 
length does not increase friction; say for water-wheels, 
journals of from 8 to 14 inches. 

Cad wall ader Evans. 

Oliver Evans. 

June 15, 1826. 


24 


370 


APPE NDIX. 


WATER-WHEELS. 

On the construction of Water-wheels , and the method of ap¬ 
plying the icater for propelling them , so as to produce 
the greatest effect 

The following article is from the pen of a practical 
engineer of experience and talents; his observations 
are, in general, in perfect accordance with those of the 
editor. The principles which he advocates are un¬ 
doubtedly correct, and it is hoped their publication in 
this work will induce some of our most intelligent mill¬ 
wrights to forsake the beaten track, and to practise the 
modes recommended. Let them recollect that Mr. Par¬ 
kin was not a mere theorist, hut a practical man, like 
themselves. The death of this gentleman has deprived 
society of the service of one of its members, from whose 
liberality, experience, and skill, much was expected. 

■[FROM T1TE FRANKLIN JOURNAL.] 

In constructing water-wheels, especially those of great 
power, the introduction of iron is a most essential im¬ 
provement, and if this metal, and artisans skilled in 
working it, could be obtained at reasonable rates, water¬ 
wheels might be made wholly of it, and would prove, 
ultimately, the cheapest; for if managed with due care, 
and worked with pure, (not salt) water, they would last 
for centuries; but, as the first cost would be an objec¬ 
tion, I would recommend, in all very large wheels, that 
the axis be made of cast-iron; and, in order to obtain 
the greatest strength with the least weight, the axis or 
shaft ought to be cast hollow, and in the hexagon or 
octagon form, with a strong iron flanch, to fix each set 
of arms and the cog-wheel upon; these flanches to be 
firmly fixed in their places with steel keys. 

On the adaptation of water-wheels to the different 
heights of the water-falls by which they are to be worked, 
I will remark that falls of from 2 to 9 feet are most ad- 


APPENDIX. 


371 


vantageously worked with the undershot wheel; falls of 
10 feet and upwards, by the bucket or breast-wheel, 
which, up to 20 or 25 feet, ought to be made about one- 
sixth higher than the fall of water by which it has to be 
worked; and in wheels of both descriptions, the water 
ought to How on the wheel from the surface of the dam. 
[ am aware that this principle is at direct variance 
with the established practice, and perhaps there are few 
wheels in these States that can be worked, as they are 
now fixed, by thus applying the water: the reasons will 
be apparent from what follows. 

In adjusting the proportions of the internal wheels by 
which machinery is propelled, it is necessary, in order 
to obtain the greatest power, to limit the speed of the 
skirt of the water-wheel, so that it shall not be more than 
from 4 to 5 feet per second; it having been ascertained, 
by accurate experiments, that the greatest obtainable 
force of water is within these limits. As a falling body, 
water descends at the speed of about 16 feet in the first 
second, and it will appear evident that if a water-wheel 
is required to be so driven, that the water with which 
it is loaded has to descend 10,11, or 12 feet per second, 
at which rate wheels are generally constructed to work, 
a very large proportion of the power is lost, or, rather, is 
spent, in destroying, by unnecessary friction, the wheel 
upon which it is flowing. 

In the common way of constructing mill-work, and of 
applying water to wheels, it has been found indispensa¬ 
bly necessary to have a head of from 2 to 4 feet above 
the aperture through which the water flows into the 
buckets, or against the floats of a water-wheel, in order 
to be able to load the wheel instantaneously, without 
which precaution it could not be driven at the required 
speed: from this circumstance it has been erroneously in¬ 
ferred, that the impulse or shock which a water-wheel 
so fllled receives, is greater than the power to be derived 
from the actual gravity of the water alone. This theory 
I have heard maintained among practical men; but it is, 
in fact, only resorting to one error to rectify another. 
Overshot wheels have been adopted, in numerous cases, 
merely for the purpose of getting the water more readi- 


APPENDIX. 


o 70 
O k lx 

ly into the buckets; but confine the wheel to the pro¬ 
per working speed, and that dilficulty will not exist. 

In consequence of the excessive speed at which wa¬ 
ter-wheels are generally driven, a small accumulation 
of back water either suspends or materially retards their 
operations; but, by properly confining their speed, the 
resistance from back water is considerably diminished, 
and only amounts to about the same thing as working 
from a dam as many inches lower as the wheel is im¬ 
mersed; and in undershot wheels, worked from a low 
head, or situated in the tide-way, the resistance from 
back water may be farther obviated by placing the floats 
not exactly in a line from the centre of the wheel, but 
deviating 6 or 8 inches from it, so as to favour the wa¬ 
ter in leaving the ascending float. 

In constructing water-wheels to be driven at the speed 
of 4 or 5 feet per second, it will be requisite to make 
them broader to work the same quantity of water which 
is required to drive a quick-speeded wheel. Thus, if a 
person intending to erect a mill, has a stream sufficient 
to work a wheel 5 feet broad, the skirt to move 10 feet 
per second, it is evident that if he wishes to work all 
the water which such wheel takes, he must have his 
wheel 10 or 12 feet broad, instead of 5, otherwise the 
water must run to waste, as there would not be room 
in a slow-moving vdieel of 5 feet broad to receive more 
than half of it. The principal advantages resulting 
from the proposed method of adapting wheels to the 
falls by which they are to be worked, and the method 
of applying water are— 

1. The lessening of friction upon the main gudgeons, 
(and first pair of cog-wheels,) by which, with a little 
care, they may be kept regularly cool, and the shaft or 
axis be preserved much longer in use than when the 
gudgeons cannot be kept cool. 

2. By working water upon the principle of its actual 
gravity alone, and applying it always at the height of 
the surface of the dam, its power is double what is ob¬ 
tained by the common method of applying it. 

3. The expensive penstock required to convey the 
water to the wheels, generally used, will not be needed, 


APPENDIX. 


373 


as one much shallower, and consequently less expensive, 
will be sufficient. 

4. The resistance of back water is reduced as far as 
possible. 

5. The risk of fire is less, as the friction is reduced. 

TV. Parkin, Engineer. 

September 2\th, 1825. 


That water, whenever the fall is sufficient, ought al¬ 
ways to be applied upon the principle of its actual gravity, 
appears to be a conclusion so obvious, that it is asto¬ 
nishing it should ever be disputed. The acknowledged . 
difference between the effect of overshot and undershot 
wdieels, is an evidence of the truth of the principle. The 
whole moving power of water is derived from its gravity: 
it is this which causes it to fall, and although in falling 
from a given height it acquires velocity, its gravitating 
force remains the same, and all the effect which this 
might have produced has been expended upon itself, 
and not in moving any other body. The force with 
which water strikes, after it has fallen from any height, 
is calculated to deceive those who are not well grounded 
in the principles of hydrostatics; but it is admitted, both 
by Mr. Evans and Mr. Ellicott, that the effect upon over¬ 
shot wheels is diminished by increasing the head, and 
the reason given for leaving the head so great as they 
prescribe, is the necessity of filling the buckets with 
sufficient rapidity; this necessity, however, is created 
by giving too much velocity to the wheel. 

It has been stated by Mr. Evans, and is generally be¬ 
lieved by mill-wrights, that it is necessary to give a much 
greater velocity to wheels, than that which is recom¬ 
mended by Smeaton and others, in order to cause the 
mill to run steadily, and prevent its being suddenly 
checked by an increased resistance. This is saying that 
the water-wheel ought to be made to operate as a fly¬ 
wheel, which it will not do if its motion be slow. The 
objection to this is twofold. By giving to the skirt of 



374 


APPENDIX. 


the wheel a motion much exceeding 4 or 5 feet per se¬ 
cond, its power is considerably reduced below the maxi¬ 
mum, and this loss of power is perpetual; wasting a con¬ 
siderable portion of water, to convert the water-wheel 
into a fly-wheel, which water might be employed in 
giving greater power to the mill. When a mill, from 
the nature of the work which it has to perform, requires 
the action of a fly-wheel, the situation of the water-wheel 
is often the worst that could be devised for this purpose, 
especially where there is any considerable gearing in 
the mill. A fly-wdieel does not add actual power, but it 
serves to collect power, where the resistance is unequal; 
and in order to its producing this effect most perfectly, 
it ought to be placed as near as possible to the working 
part of the machinery. In grist mills there is no neces¬ 
sity for a fly-wheel; the stones perform this office in the 
most effectual manner, and the same remark is applica¬ 
ble to every kind of mill without a crank, and in which 
the resistance is equal, or nearty so, during the whole 
time of its action. 

Although we have spoken highly of the general views 
given by Mr. Parkin, in his communication to the 
Franklin Journal, he has fallen into some mistakes, 
which were pointed out by a writer in the same publi¬ 
cation, Yol. IV., page 166. A part of this communi¬ 
cation is subjoined, as it contains remarks, and a tabular 
view of the velocities attained, and the distances fallen 
through, by bodies, in fractional parts of a second, which 
may be of great practical utility^:— 

“ I suppose that, at the present day, no man who pro¬ 
fesses to be capable of directing the construction of a water¬ 
wheel, or of estimating the amount of a water power, 
is ignorant of the fact, that water falls through a 
distance of about sixteen feet in the first second. But I 
suspect that many who assume the above qualifications, 
do not know the ratio of increase, either in the distance 
or the velocity. I have drawn this conclusion, not only 
from conversations with several practical engineers, but, 
also, from essays published in our scientific journals. As 
an instance of the latter, I will select, for its convenience 


APPENDIX. 


375 


of reference, an article on water-wheels, published in 
this Journal, (vol. ii. page 103,) which being the produc¬ 
tion of a practical engineer, and having passed the in¬ 
spection of a scientific committee, may be considered 
as corroborating my commencing observations. In the 
third paragraph of that article is the following sentence: 
4 As a falling body, water descends at the speed of near¬ 
ly 16 feet in the first second, and it will appear evident, 
that if a water-wheel is required to be so driven, that 
the water with which it is loaded has to descend 10,11, 
or 12 feet per second, at which rates wheels are gene¬ 
rally constructed to work, that a very large proporticm 
of the power is lost.’ 

66 Here, in the first place, we find speed or velocity , con¬ 
founded with the distance fallen in the first second; 
whereas, the latter is 16 feet, and the former is accele¬ 
rated, from nothing, at the commencement, to 32 feet 
per second, at the end of the first second; so that this 
part of the sentence conveys, strictly, no intelligible 
meaning; it is, nevertheless, made a standard by a com¬ 
parison between which, and any given velocity of a wa¬ 
ter-wheel, we are to infer the loss of power sustained 
through excess of speed; thus, in the case of a wheel 
whose velocity is 10 or 12 feet per second, comparing 
these numbers with the mysterised number 16, the 
writer concludes, ‘ that a very large portion of the pow¬ 
er is lost.’ The height of the fall which indicates the 
whole amount of the power, is not mentioned, but sure¬ 
ly, to estimate the proportion between a defined part, 
and undefined whole, is impossible. 

$ $ $ & & & $ 

“ I have made a calculation of the distances and ve¬ 
locities attained by falling bodies, in various fractional 
parts of a second, which is here introduced for the in¬ 
formation of those practical and theoretical engineers 
who have avoided the labour of doing it for themselves. 

“I have proceeded on the following established data; 
namely:— 

“ Heavy bodies fall through a distance of 16 feet, in 
the first second: at the end of which they have acquired 


37G 


APPENDIX 


a velocity of 32 feet per second. The velocity increases 
as the times—the distance increases as the square ol 
the times. 


Time of Descent. 

Distance fallen. 

Velocity attained 
per second. 



feet. 

inches. 

feet. 

inches. 

V 

• • 

0 

0 1-90 

0 

3 

2 

• • 

0 

0 1-21 

0 

6 

3 

• • 

0 

0 2-19 

0 

9 

4 ^ 128th of a sec. 

0 

0 3-16 . 

1 

3 

5 

• • 

0 

0 2-7 

1 

6 

• • 

0 

0 2-5 

1 

6 

7 

• • 

■ 0 

0 3-5 

‘ 1 

9 

2 1 


0 

0 3-4 

2 


3 

• • 

0 

1 2-3 

3 


5 

> 32nds of a sec. 

0 

0 

3 

4 2-3 

4 

5 


6 

• • 

0 

6 3-4 

6 


7 J 

• • 

0 

9 1-4 

7 



l-4th of a sec. 

1 

0 

8 



• • 

1 

3 1-6 

9 


10 

• • 

1 

6 3-4 

10 


11 

• • 

1 

10 2-3 

11 


12 

>32nds of a sec. 

2 

3 

12 


13 

• • 

2 

7 2-3 

13 


14 

• • 

3 

0 3-4 

14 


15 J 

• • 

3 

6 2-11 

15 

• 


1 half of a sec. 

4 

0 

16 


17 1 

• • 

4 

6 1-5 

17 


18 

• • 

5 

0 2-3 

18 


19 

• • 

5 

7 2-3 

. 19 

j 

20 ^32nds of a sec. 

6 

3 

20 


21 

• • 

6 

10 2-3 

21 


22 

• • 

7 

6 3-4 

22 


23 

• • 

8 

3 1-5 

23 

• 


3-4ths of a sec. 

9 

0 

24 


25'] 

• • 

9 

9 1-5 

25 


26 

• • 

10 

6 3-4 

26 


27 

• • 

11 

4 2-3 

27 


28 

^*32nds of a sec. 

12 

3 

28 


29 

• • 

13 

1 2-3 

29 


30 

• • 

14 

0 3-4 

30 


31 J 

• • 

15 

0 1-5 

31 


1] 

• • 

16 


32 


2 

15 

>seconds. 

| 

64 

3600 


64 

480 


30 


14400 


960 


1 minute. 

57600 


1920 



“To determine what proportion of a given water 
power is lost by a given velocity of the wheel it is only 





























APPENDIX. 


necessary to ascertain what distance the water must de¬ 
scend to acquire that velocity. Then this distance, com¬ 
pared with the wdiole fall, answers the question. Thus: 
suppose the whole fall to be 10 feet, and the velocity of 
the wheel 4 feet per second; this velocity is due to a fall 
of 3 inches, or one-fortieth part of the whole fall, which 
is the proportion sought. Or, suppose the velocity to be 
13 feet per second, which is due to a fall of 2 feet 7f 
inches, then the loss is rather more than one-fourth of 
the whole fall of ten feet. But it must be especially 
noted, that these estimates embrace the supposition, that 
the water issues upon the wheel in the direction of the 
motion of its skirt, and precisely at that distance below 
the surface of the dam which answers to the velocity 
of the wheel. Inattention to this particular is a very 
important and frequent cause of loss. L. M.” 

With respect to the actual advantage of giving to over¬ 
shot wheels a motion much less rapid than that usually 
given, the following example will probably have more 
effect on the mind of the mere practical workman, than 
any reasoning that could be offered: and, in fact, rea¬ 
soning would be of little value, were it not supported 
by practical results. 

The subjoined account is from the Technical Repo¬ 
sitory, a work published in London:— 

“ On the comparcdive Advantages of different Water- 
Wheels , erected in the United States of America , by 
Jacob Perkins, Esq.; and in this country , by Mr. 
George Manwaring, Engineer. 

“ Mr. Perkins erected at Newbury port, a water-wheel, 
of 30 feet in diameter, on the plan of what is termed, 
in America, a pitch-bach; but in this country a bach- 
shut ; that is, one which receives the water near to its 
top, but not upon it, as in overshot-wheels; this is, in¬ 
deed, the most judicious mode of laying water upon the 
wheel; as, in case of floods, the wheel moves in the same 
direction with the water, and not in the opposite one; 
neither is it encumbered, as in the overs/^-wheel, with 


APPENDIX. 


o^n 

o (o 

a useless load of water at its top,where it does nothing 
but add to the weight upon the necks or pivots of the 
wheel-shaft, and to the consequent loss of power by the 
increased friction upon them; whereas, in the pitch-back, 
or back-shut wheel, the water is laid on at a point where 
it acts by its leverage in impelling the wheel, and has 
yet time to become settled in the buckets previously to 
its reaching the point level with the axis, where it acts 
with its greatest power. The wheel itself was construct¬ 
ed of oak; but with iron buckets; and it had a ring of 
teeth around it, which drove a cast-iron pinion, of three 
feet in diameter, which gave motion to three lying shafts, 
each of thirty feet in length, coupled together, so as to 
form a line of ninety feet; and from which the necessary 
movements were communicated to the machinery for 
making nails. 

“Mr. Perkins placed his pinion as close as possible un¬ 
der the pen-trough, which delivered the water upon the 
wheel; and he thus greatly lessened the weight upon the 
necks or gudgeons of the wheel-shaft, by suspending it, 
as it were, upon the pinion; whereas, had he, as is usual, 
placed it on a horizontal line with the axis of the wheel, 
and on the opposite side of it, he would have loaded the 
necks with a double weight; namely, the water upon one 
side of the wheel, and the resistance opposed by the ma¬ 
chinery to be driven by it on the other. He also took 
care that the teeth upon the wheel, and the pinion, 
should always be kept wet,, or run in water, instead of 
being greased, as is usual, and this he found sufficient to 
cause them to run smoothly and without the least noise. 
The motion of the wheel’s periphery was about three 
feet per second, agreeably to the improved theory, so 
ably demonstrated by the late scientific Mr. Smeaton; 
and it continued to perform its work, with great satis¬ 
faction to its owners, for ten years, when it was unfor¬ 
tunately destroyed by fire. 

“An opportunity soon presented itself of comparing 
the advantages 'of this watcr-wlieel with another, which 
the proprietors were induced to erect on the representa¬ 
tions of a mill-wright, that the wheel was too high, and 
that it w T ould be much better, were it only twenty-three 
feet in diameter, and received its water at the breast. 


APPENDIX. 


379 


The trial, however, proved, that in driving the nail ma¬ 
chinery, which had escaped the fire that destroyed the 
water-wheel, the new wheel required twice the quantity of 
water to work it which actuated the former one , and only 
did the same work. 

u Mr. Man waring has also had an opportunity of veri- 
lying, in this country, the advantages of a construction 
similar to Mr. Perkins’s, in a cast-iron hacJz-shut water¬ 
wheel of the same diameter as his, (namely, thirty feet,) 
and which also has a ring of teeth around it, driving a 
pinion of three feet in diameter, posited on the same side 
of the wheel as Mr. Perkins’s, but not quite so high, it 
being a little above the centre of the wheel, and the 
teeth of the wheel and pinion are always kept wet. 
This wheel is employed in grinding flour, at a corn-mill 
in Sussex, and drives six pairs of stones, besides the other 
necessary machinery, it moving at the rate of about 
three feet per second; and so great satisfaction has it 
given, that Mr. Manwaring is now constructing another 
water-wheel upon the same plan, and for the same pro¬ 
prietor; only that it will be wider, and is calculated to 
drive eight pairs of stones. 

“We are glad to have this opportunity of communi¬ 
cating these valuable practical facts: the same results 
being also obtained in two countries so widely separated 
as the United States and England, make them more va¬ 
luable; and prove, that when persons think rightly, they 
will naturally think alike,” 


The foregoing example, although it relates to a pitch- 
hack wheel, may serve our purpose as well as if it had 
been an overshot; there being an evident similarity be¬ 
tween an overshot, with the water delivered on the top, 
with but little head, and the pitch-back , as constructed 
by Mr. Perkins; and also, between an overshot with 
considerable head, and the breast-wheel. 

The remarks made upon pitch-back wheels, are wor¬ 
thy the serious attention of the mill-wriglit. Mr. Evans 
very correctly compares them, in their action, to over- 



380 


APPENDIX. 


shots: Mr. Ellicott thinks “an overshot with equal 
head and fall is fully equal in power,’’ and has dismissed 
them in a very few words. The reason of this is evi¬ 
dent; the head , which they thought to be necessary, was 
not so easily managed with the pitch-back as with the 
overshot; but when it is admitted that the water should 
be delivered at the surface of the dam, that the velocity 
of the wheel should not exceed 4 or 5 feet per second, 
and that its capacity for containing water should be in¬ 
creased, the difficulty vanishes altogether. The water, 
when emptied from the buckets, has its impulse in the 
right direction to carry it down the tail-race; and in 
case of back-water, the greater facility with which it 
will move is undeniable. 

With respect to undershot wheels, Mr. Evans con¬ 
cludes that they ought to move with a velocity nearly 
equal to two-thirds of that of the water, and Mr. Ellicott 
estimates the velocity at quite two-thirds. It would be 
saying but little to assert that this did not agree with 
theory; but it does not accord with the opinions of many 
intelligent and experienced mill-wrights. It was as¬ 
serted, upon theory, that the power of an undershot 
wheel would be at a maximum, when the velocity of the 
floats of the wheel was equal to one-third of the velocity 
of the water: practice, however, did not confirm the 
truth of this theory; and Borda has shown that the con¬ 
clusion was theoretically incorrect, applying only to the 
supposition that the water impelled a single float-board; 
but that in the action upon a number of float-boards, as 
in a mill-wheel, the velocity of the wheel will be one-half 
the velocity of the water, when the effect is a maximum. 
The demonstration of this may be seen under the article 
Hydrodynamics, in the Edinburgh Encyclopedia. This 
was fully confirmed by the experiments of Smeaton, who, 
in speaking upon them, observes, that “in all the cases 
in which most work is performed in proportion to the 
water expended, and which approach the nearest to the 
circumstances of great works, when properly executed, 
the maximum lies much nearer to one-half than one- 
tliird, one-half seeming to be the true maximum.” 


APPENDIX. 


381 


The succeeding observations are extracted from “Prac¬ 
tical Essays on Mill-work, and other Machinery, by 
Robertson Buchanan.” Cast iron is very generally em¬ 
ployed in England, not only for the wheel-work of mills, 
but, also, for many parts of the framing; the same prac¬ 
tice obtains in those parts of our own country where 
castings can be secured with facility, and will gain 
ground as its real value becomes known. Of course, 
the following extracts apply, in many instances, to the 
use of this material; but it will be found that the prin¬ 
ciples upon which they are founded will, in general, ap¬ 
ply to wood as well as to iron. 

u A Practical Inquiry respecting the Strength and Durabi¬ 
lity of the Teeth of Wheels used in Mill-work. 

“ Having treated of the forms of the teeth of wheels, 
I come now to consider their proportional strength, with 
relation to the resistance they have to overcome. 

“ I am aware, that owing to a great variety of circum¬ 
stances, this subject is involved in much difficulty, and 
that it is no easy task to form any general rule with re¬ 
gard to the pitches and breadths of the teeth of wheels. 
I do not pretend to more than a mere approximation 
towards general rules; yet, were this judiciously done, I 
am of opinion that it might be useful to the mill-wright 
who has not had leisure or opportunity for scientific in¬ 
quiries. A rule, though not absolutely perfect, is better 
in all cases than to have no guide whatever. 

“And it is too evident to require proof that it is es¬ 
sential to the beauty and utility of any machine, that 
the strength and bulk of its several parts be duly pro¬ 
portioned to the stress or wear to which the parts may 
be subject. 

“Some general observations on the wheel-work of 
mills will serve greatly to simplify our inquiries on the 
subject. 


382 


APPENDIX. 


“ General Observations on the Wlieel-worh of Mills . 

“ Mistaken attempts at economy have often prompted 
the use of wheels of too small diameter. This is an 
evil which ought carefully to be avoided. Knowing the 
pressure on the teeth, we cannot with propriety reduce 
the diameter of the wheel below a certain measure. 

“ Suppose, for instance, a water-wheel of 20 horses’ 
power, moving at the pitch line with a velocity of 3£ 
feet per second. It is known that a pinion of 4 feet di¬ 
ameter might work into it without impropriety; but we 
also know that it would be exceedingly improper to sub¬ 
stitute a pinion of only one foot diameter, although the 
pressure and velocity at the pitch lines, in both cases, 
would be, in a certain sense, the same. In the case of 
the small pinion, however, a much greater stress would 
be thrown on the journeys (or journals ,) of the shaft. 
Not, indeed, on account of tortion or twist, but on ac¬ 
count of transverse strain arising as well from greater 
direct pressure, as from the tendency which the oblique 
action of the teeth, particularly when somewhat worn, 
would have to produce great friction, and to force the 
pinion from the wheel, and make it bear harder on the 
journals. The small pinion is also evidently liable to 
wear much faster, on account of the more frequent re¬ 
currence of the friction of each particular tooth. 

“ That these observations are not without foundation, 
is known to mill-wrights of experience. They have 
found a great saving of power by altering corn mills, 
for example, from the old plan of using only one wheel 
and pinion, (or trundle ,) to the method of bringing up 
the motion by means of more wheels and pinions, and 
of larger diameters and finer pitches. 

“The increase of power has often, by these means, 
been nearly doubled, while the tear and wear has been 
much lessened; although it is evident, the machinery, 
thus altered, was more complex. 

“ The due consideration of the proper communication 
of the original power, is of great importance for the con¬ 
struction of mills, on the best principles. It may easily 


APPENDIX. 


383 


be seen, that in many cases a very great portion of the 
original power is expended, before any force is actually 
applied to the work intended to be performed. 

“ Notwithstanding the modern improvements in this 
department, there is still much to be done. In the 
usual modes of constructing mills, due attention is sel¬ 
dom given to scientific principles. It is certain, how¬ 
ever, that were these principles better attended to, 
much power, that is unnecessarily expended, would be 
saved. In general this might be in a great measure ob¬ 
tained by bringing on the desired motions in a gradual 
manner, beginning with the first very slow, and gradu¬ 
ally bringing up the desired motions by wheels and pi¬ 
nions of larger diameters. This is a subject which should 
be well considered, before we can determine, in any par¬ 
ticular case, what ought to be the pitch of the wheels. 
In the case above alluded to, where the supposition is a 
pinion of 4 feet diameter, or of 1 foot diameter, it is ob¬ 
vious that the same pitch for both would not be prudent: 
that for the small pinion ought to be much less than 
that which might be allowed in the case of the larger 
pinion. It is also equally obvious that the breadth of 
the teeth, in the case of the small pinion, ought to be 
much greater than that in the case of the larger pinion. 

“It is evident, however, that although great advan¬ 
tage may often be derived from a fine pitch, that there 
is a limit in this respect, as also with regard to the 
breadth. We shall endeavour to find some trace of this 
in what follows: and, that we may the better do this, 
we shall call in the aid of propositions, which are true 
with respect to pieces of timber, or metal, subjected to 
ordinary causes of pressure. It is allowed that they 
cannot here, in strictness, be demonstrated, as applicable to 
wheel-work. Yet they will, for want of better light, serve 
at least to prevent any material, practical error, with re¬ 
gard to the strength of the teeth of the wheels. For it 
is to be remembered, that we are not so much here m 
search of truths of curious or profound mathematical 
speculation, as of that kind of evidence of which the 
subject admits, and which may be sufficiently satisfac¬ 
tory for any practical purpose. 


384 


APPENDIX. 


“ As cast iron pinions are now generally used, and as 
the teeth of the pinion are most subject to wear, I think 
we are safe in the present inquiry, in considering them 
all as cast iron. 

“The laws to which I have alluded in this investiga¬ 
tion, are these:— 

“ ‘ Principles of proportioning the Strength of Teeth of 

Wheels. 

“ < PROPOSITION I; 

“ ‘The strength of any Piece of Timber or Metal , whose 
section is a Rectangle , is in direct proportion to the breadth , 
and as the square of the depth 

“Hence, may be inferred, that the strength of the 
teeth of wheels, moving at the same velocity, and un¬ 
der the same circumstances, is directly in proportion to 
their breadth, and as the square of their thickness. 
Thus, for example, if we double the breadth, we only 
double the strength; but if we double the thickness, or, 
in other words, double the pitch, keeping the original 
breadth, we increase the strength four times. 

“ For although, when wheels are working accurately, 
the strain is, at the same time, divided over several 
teeth; yet as a very small inaccuracy, or even the in¬ 
terposition of any small body, such as a chip of wood, 
or stone, throws the whole stress upon a single tooth, 
in practice, therefore, and in order to simplify the case, 
we may consider the strength of a -single tooth as re¬ 
sisting the pressure of the whole work. 

“But as the length of the teeth commonly varies 
with the pitch, this circumstance must be taken into ac¬ 
count, and the most simple view we can take of it seems 
to be that of having the strain of each tooth thrown all 
to the outward extremity; we have then the following 
proposition to guide this part of our inquiry:— 

. PROPOSITION II. 

“ ‘ If any force be applied laterally to a Lever or Beam, 


* See Emerson, Prop. 67. 


APPENDIX. 385 

the Stress upon any plate is directly as the Force and its 
distance from that plate.’* 

“ ‘ PROPOSITION III. 

u 6 The Pitch being the same, the Stress is inversely as 
the Velocity 

“ For example—if the pitch lines of one pair of wheels 
be moving at the rate of 6 feet in a second, and another 
pair of wheels, in every other respect under the same cir¬ 
cumstances, be moving at the rate of 3 feet in a second, 
the stress on the latter is double of that on the former.” 


“ Of arranging the Numbers of Wheel-Worh. 

“ In a machine, the velocity of the impelled point 
should be to that of the working point, in the ratio 
which is adapted to the maximum effect of the moving 
power on the one part, and the best working effect on 
the other part. Any other arrangement of the relative 
motions of the parts of a machine must clearly be at¬ 
tended with a loss of power, or the work will not be 
done properly. But when the best working velocity is 
known, and, also, that which enables the first mover to 
produce the greatest effect, the proper arrangement of 
the numbers of the teeth of the wheels and pinions is 
a very simple operation. 

“ It will be an advantage to advertise the young me¬ 
chanic of one or two essential particulars, before pro¬ 
ceeding to the principal object. 

“ In the first place, when the wheels drive the pinions, 
the number of teeth in any one pinion should not be 
less than 8; but rather let there be 11 or 12, if it can 
be done conveniently. And in the particular form of 
teeth previously described, the number of teeth in a pi¬ 
nion should not be less than 10; but it would be better 
to have 13 or 14. 

“ Secondly,—When the pinions drive the wheels, the 
number of teeth on a pinion may be less: but it will not 




• See Emerson, Prop. 69. 

25 


t See Emerson, Prop. 119,'Rule 8. 



386 


APPENDIX. 


in any case be desirable to have fewer than 6 teeth on 
a pinion; and give the preference to 8 or 9, where it 
can be done with convenience. 

“ Thirdly,—The number of teeth in a wheel should be 
prime to the number of teeth in its pinion, that is, the 
number representing the teeth in the wheel should not 
be divisible by the number of teeth in the pinion with¬ 
out a remainder. And as the number of pinions will, 
in general, be first settled, it will be an advantage to 
take a prime number for each pinion, as 7,11,13,17,19, 
23, &c., because such numbers are more seldom factors 
than others. But when it happens that a prime num¬ 
ber can be directly fixed upon for the wheel, any whole 
number which approaches near to the required ratio 
will answer for the pinion; as minute accuracy is not 
required. A prime number for the wheel, or one which 
is not divisible by the number of the pinion, is esteemed 
the best, because the same teeth will not always come 
together, and the wear will be more uniform. 

“ Fourthly,—If it be desired that a given increase or 
decrease of velocity should be communicated, with the 
least quantity of wheel-work, it has been shown that 
the number of teeth on each pinion should be to the 
number on its wheel, as 1 : 3.59 (Dr. Young’s Nat. Phil., 
Yol. II., Art. 366.) But, on account of the space re¬ 
quired for several wheels, and the expense of them, it 
will often be necessary to have 5 or 6 times the number 
of teeth on the wheel that there is on the pinion. The 
ratio of 1 : 6 should, however, not be exceeded, unless 
there be some other important reason for a higher ratio.” 


“Practical Observations with regard to the making of Pat¬ 
terns of Cast Iron Wheels. 

“ Having determined the pitch of the wheel strong 
enough for the purpose to which it is to be applied, the 
thickness of the tooth serves to regulate the proportion¬ 
ate strength of the other parts. 



APPENDIX. 


387 


u A very respectable mill-wright informs me that he 
has for a considerable time adopted the following rule 
for determining the length of the teeth of wheels, the 
practical efficacy of which he has found quite satisfac¬ 
tory : 

“ Rule —Make the length of the teeth equal to the pitch, 
deducting freedom, (by the freedom is meant the distance 
at the top of one tooth and the root of another, mea¬ 
sured at the line of centres,) in other words, the distance 
from root to root of the teeth, at the line of teeth, when 
the wheels are in action, exactly equal to the pitch. 

“For example: he makes the teeth of two inches 
pitch, one inch and thirteen-sixteenths in length, which 
is allowing three-sixteenths of freedom. 

“ Another respectable mill-wright, who has had much 
experience, particularly in mills moved by horses, has, 
for a considerable time past, made the teeth of his wheels 
only one-half of the pitch in length, and works them as 
deep as possible, without the point touching the bottoms. 
Before he fell on this expedient, he found the teeth ex¬ 
ceedingly liable to be broken from any sudden motion 
of the horses. 

“ Indeed, upon reflection, it will be found that there 
is no occasion for more freedom than that the point of 
the tooth of the one wheel shall just clear the ring of 
the other: more than this must only serve to weaken 
the teeth. The mode of gearing, however, above alluded 
to, is more necessary in horse mills than where the 
moving power is steady and regular. 

“ Hutton (on clock-work) recommends making the dis¬ 
tance of the pitch line three-fourths of what we call the 
thickness of the tooth. Thus, suppose the rule applied 
to a two inch pitch, and that the tooth and space were 
exactly equal, then the tooth would project three-fourths 
of an inch beyond the pitch line, and its root would be as 
far within the pitch line, as to receive freely the tooth 
intended to act on it; suppose it also three-fourths, then 
the tooth would be one and a half inch long, besides the 
freedom, which making, as above, three-sixteenths, the 
tooth would be in all one and eleven-sixteenths inch long. 


388 


APPENDIX. 


“But it is to be remarked, that the mill-wright, in 
making his pattern for a cast iron wheel, has to attend 
to a circumstance arising from the nature of that mate¬ 
rial. The pattern must not only be of such a form as 
to be sufficiently strong, calculating by the bulk of the 
parts, but also proportioned, so that when the fluid 
metal is poured in the mould, it may cool in every part 
nearly at the same time. 

“ When due attention is not paid to this circumstance, 
as the metal is cooling, if it contract faster in one part 
than in another, it will be apt to break somewhere, just 
as a drinking glass is broken by suddenly cooling or 
heating in any particular part of it. In all patterns for 
cast iron, about one-eighth of an inch to the foot should 
be allowed for the contraction of the metal in cooling. 

“Attention must also be paid to taper the several 
parts so that they may rise freely without injuring the 
mould when the founder is drawing them out of the sand. 
A little observation of the operations of a common 
foundry, will better instruct in this part of the subject 
than many words. We may observe, however, that 
about one-sixteenth of an inch, in a depth of 6 inches, 
is commonly a sufficient taper. 

“Attending to those circumstances, I beg leave to 
offer the following proportions as having been found to 
answer in practice. 

“ Make the thickness of the ring equal to the thick¬ 
ness of the tooth near its root. When the ring is made 
thinner than the root of the tooth, the ring commonly 
gives way to a strain which would not break the tooth. 

“Make the arm, at the part where it proceeds from 
the ring, of the same breadth and thickness as the ring, 
and, at the junction, let it be so formed as to take off any 
acute angle which would be apt to break off in the sand. 

“The arms should become larger as they approach 
the centre of the wheel, (see Emerson, Prop. 119, Buie 
8,) and the eye should be sufficiently strong to resist 
the driving of the wedges, by means of which it is to 
be fixed on the shaft. This cannot be brought easily to 
calculation. 


APPENDIX. 3§9 

“On the other hand, care must be taken not to make 
the eye so thick as to endanger unequal cooling. 

“Itshould be somewhat broader than the breadth of 
the teeth, in order that it may be the firmer on the shaft: 
this breadth must be greater in proportion as the wheel 
is large. 

o 

“When the ring is about an inch thick, it is common 
to make the eye about an inch and a quarter in thick¬ 
ness, and about one-fifth broader than the ring, when 
the wheel is about four feet in diameter. 

“ Small wheels have generally but four arms, but it 
being improper to have a great space of the ring un¬ 
supported, the number of arms should be increased in 
large wheels. 

“In order to strengthen the arms with little increase 
of metal, it is not unusual to make them feathered, 
which is done by adding a thin plate to the metal at 
right angles to the arm. 

“The same rules apply to bevelled wheels; of the 
practical mode of laying down the working drawings of 
which we have already spoken. But it is proper to ob¬ 
serve that the eye of a bevelled wheel should be placed 
more on that side which is farthest from the centre of 
the ideal cone, of which the wheel forms a part. 

“ When wheels are beyond a certain size, it becomes 
necessary to have patterns sometimes made for them, 
cast in parts, which are afterwards united by means of 
bolts. 

“A very good mode to prevent the bad effects of une¬ 
qual contraction, is to have the arms curved; the curved 
parts are commonly of the same radius as the wheel, 
and spring from the half length of the arms.” 


“ Of Malleable or Wrought Iron Gudgeons. 

“ Professor Robinson states,* that the cohesive force 
of a square inch of cast iron is from 40,000 to 60,000 
lbs., wrought iron from 60,000 to 90,000 lbs. 

“In the year 1795, I had occasion to substitute cast 

* Encyclopaedia Britannica, article Strength of Materials, 40. 



390 


APPENDIX. 


iron gudgeons for those of wrought iron, and made some 
experiments on those metals, from which I drew the 
following inference:— that gudgeons of the same size , of 
cast and of wrought iron , in practice , are capable , at a me¬ 
dium, of sustaining weights loithout flexure in the propor¬ 
tion of 9 to 14. 

“ Taking it for granted that this proportion is near 
the truth, we may find the diameter which any wrought 
iron gudgeon ought to have when its lateral pressure is 
given, in the following manner:— 

“1. Find the diameter which a cast iron gudgeon 
should have to sustain the given pressure; then say, as 
14 is to the cube of the diameter of the cast iron gud¬ 
geon, so is 9 to the cube of the diameter of the wrought 
iron gudgeon. 

“2. The root of this last number gives the diameter 
required of the wrought iron gudgeon. 

EXAMPLE. 

“ Suppose the lateral pressure to be 125 hundred 
weights, the cube root of which is 5, the diameter in 
inches of the cast iron gudgeon: then say, 

As 14 
is to 125 
so is 9 
to 80,357 

The cube root of which is 4.30887.” 


“ Of the Bearing of Shafts. 

“ The bearings on which gudgeons and journals rest 
and revolve, are sometimes termed Pillows , and fre¬ 
quently Brasses , from being often made of that sub¬ 
stance. 

a It has become general to fix pillows in blocks of cast 
iron. Hence, the term, Pilloio Bloch , and sometimes, 
corruptly, Plumber Bloch. 

“ At the cotton works of Deanston, near Down, a wa¬ 
ter-wheel has run nearly 30 years on pillows of cast 
iron, with little sensible wear on the gudgeons, nor were 
they ever found liable to heat. 



APPENDIX. 


391 


“ The outer skin of cast iron, particularly when cast 
in metallic moulds, is remarkably hard, and it is reasona¬ 
ble to suppose that it would make a durable pillow, as 
we have seen is the case in the above instance.” 


“ On the Framing of Mill-Work. 

“ Mill-work, from its motion, occasions a tremor on all 
the parts of its framing, which subjects it to much more 
speedy decay than the mere pressure upon carpentry. 

“ Besides this general tremor, it is often subjected to 
violent, sudden thrusts, from the bad action of the wheels, 
or from reciprocating motions. 

“ It ought, therefore, to be not only sufficiently strong 
and stiff\ but sufficiently heavy , to give solidity and stea¬ 
diness. 

u Where the framing of the machinery is not firm and 
well bound, a vibratory motion in its parts, of course, 
takes place; which vibratory motion expends a conside¬ 
rable portion of the power applied. This loss of power 
is very difficult of investigation. It is certain, however, 
that whatever motion of a vibratory nature is communi¬ 
cated to the framing and objects in contact with it, (ab¬ 
stracted from the elasticity of the parts,) must be lost 
to the effect the machine would produce were the parts 
sufficiently strong and well bound together; and it is to 
be observed, that firm and well bound framing is much 
preferable to heavy framing, not so well connected in 
its parts. It is as certain, that though the framing in 
either case may be constructed so as to be equally strong, 
yet the heavy framing, from its vibration, will expend 
more of the original power than that which is less heavy, 
but firmly connected. 

“ Besides strength , stiffness , and solidity , the framing 
of mill-work requires to be constructed so as to he easy 
of repair; and so contrived, that any particular part may 
he repaired or renewed with the least possible derange¬ 
ment to the other parts of the framing. 



392 


APPENDIX. 


“ There is another circumstance in this species of 
framing which demands great attention. The shafts 
often require to he restored to their true situations , from 
which they may have deviated by the wearing of the 
parts. Now the framing ought to be so constructed as 
easily to admit of this restoration of the shafts , as also 
of any other shifting of them which may in practice be¬ 
come necessary. 

“ But though the framing which supports the parts 
of mills and machines should be firm, it is an advan¬ 
tage that the part on which any axis rests should have 
a small degree of elastic tremor, when the machine is 
in motion. Such tremor has considerable power in di¬ 
minishing the friction. It may farther be observed that 
framing to support machinery should be as independent 
of the building as possible, because the tremor it always 
communicates is exceedingly injurious.” 


On Reaction Wheels. 

These wheels were slightly noticed at page 176; and 
a description of Barker’s mill is to be found in nearly 
every work upon hydraulics, together with the improve¬ 
ment made in it by Bumsey. Within a few years past, 
wheels which operate upon the principle of the rotary 
trunk, in Barker’s mill, have been extensively brought 
into use. We are not informed by whom they were 
invented; Mr.Evans alludes to them in the first edition 
of this work, published in 1795; but it does not appear 
certain that he had then seen them; it is manifest, at all 
events, that they were not publicly known. His words 
are, “One of these is said to do well where there is 
much back water; it being small, and of a true circu¬ 
lar form, the water does not resist it much. I shall 
say but little of these, supposing the proprietors mean 
to treat of them.” 

Their great merit, certainly, is their simplicity; and 
where there is a plentiful supply of water, they may, in 
many cases, be preferable to any other. Those interest- 



393 


APPENDIX. 


Figure 1. 


ed in them aver that they are but little, if at all, infe¬ 
rior in economy to overshot mills; this, however, we are 
by no means prepared to admit. In back water they 
will undoubtedly operate better than any other, as there 
will not be any sensible loss from their wading, but only 
from the diminution of the effective head. In an eight 
feet fall, for example, should there be four feet of back 
water, the remaining four feet will produce nearly, or 
quite, its full effect. 

Many patents have been obtained for modifications 
of, and variations in, this wheel; and from the specifi¬ 
cation of one of them, as published in the Journal of the 
Franklin Institute at Philadelphia, we will give such 
extracts as will suffice to exhibit their nature and mode 
of action. In doing this, w T e shall omit the claims of 
the patentee, as this is a point with which we, in this 
place, have nothing to do. 

66 Fig. 1, a bird’s-eye view of the wheel, 
the end to which the shaft is to be at¬ 
tached, at the perforation A, being down¬ 
wards, and the open end, or rim, upwards. 

To show the floats, the upper rim, which 
covers them, is not represented. The 
lines C C exhibit the form of the floats, or 
buckets, and the manner in which they are arranged. 
The diameter of this wheel, and the width of the floats 
between the two heads, and the depth of aperture be¬ 
tween the floats, will, of course, be varied according to 
the quantity and head of water which can be obtained, 
and the purpose to which it is to be applied. The 
curved floats, it will be seen, are made to lap over each 
other; and, in practice, it has been found that the pro¬ 
portion in which they do so is a point of considerable 
importance. The proportion between the aperture and 
lap which was found to be the best, is as three to two; 
that is, for every inch of aperture, measuring from float 
to float, at the point where the water escapes, the floats 
should pass each other one and a half inch. It will be 
manifest that a slight deviation from this proportion, in 
either way, will not be attended by any sensible loss of 
power. Any considerable deviation, however, is found 
26 




394 


APPENDIX. 


to be injurious. The mechanic should be careful so to 
construct his wheel that the part of the aperture seen 
at e should be less than that seen at d. 

“ Upon the inner edge of the rim there is a projecting 
fillet, or flancli, which may be seen in the section D, of 
this wheel, at the lower part of Fig. 3, with this differ¬ 
ence, that said fillets or Handles are to be made flat as 
they are to work against, and not within, each other. 

“ Wheels so constructed may be applied either on a 
horizontal or vertical shaft, and either singly or in pairs, 
according to circumstances. 



Figure 2. 

|3h 


“Fig. 2 represents the 
double reacting wheel, 
placed on a horizontal 
shaft, in which manner A 
they are to be used,when¬ 
ever it is desirable to ob¬ 
tain motion from such a 
shaft. S is the horizontal 
shaft, A the penstock and 
B the cistern; the heads 
or sides of the cistern are 
formed in whole, or in 
part, of cast iron plates, 
securely bolted together- D D are two water-wheels, 
one of which is placed on each side of the cistern B, 
their open ends standing against the side plates of the 
cistern, which are perforated, having openings in them 
equal in size to those on the heads of the wheels, and 
being concentric with them. The fillet or flancli upon 
the rim of each wheel, is made flat, and is fitted to run 
as closely to a similar fillet or flancli on the cistern head 
as may be, without actually bearing against it, so as to 
prevent too much waste of water, and yet to avoid fric¬ 
tion by touching it. 

The size of the orifices in the wheel and cistern plates 
is a point of essential importance, and should greatly 
exceed what has been heretofore thought necessary. 
Their area should be such as to permit the whole column 
of water to act unobstructedly on the wheel, whatever 
may be the height of the head. It is found that for a 






































APPENDIX. 


395 


head of four feet, the area of the orifice should never 
be permitted to fall short of three times the number of 
square inches, which can be delivered by all the open¬ 
ings of the floats. The penstock or gateway, should 
also be sufficiently large to admit freely the same pro¬ 
portionate quantity of water through every part of its 
section; say about three times the area of the orifices 
of the cistern heads and wheels. 

“For a greater head these openings must be propor¬ 
tionally increased, or the whole intention will be de¬ 
feated, as it has been from want of attention to this 
principle that numerous failures have occurred in the 
attempt to drive mills by reaction wheels. Whenever 
it is practicable, the limit which has been given should 
be exceeded, but never can be diminished without loss. 

“ Instead of using a trunk or penstock, smaller than 
the horizontal section of the cistern B, extend the sides, 
front and back of said cistern, upwards in one continued 
line, whenever the same can be done; the cistern and 
penstock then form one trunk, of equal section through¬ 
out. 

“ When greater power is requisite, place other react¬ 
ing wheels, or pairs of wheels, upon the same shaft, so 
that each may operate in the same way. 

“ Fig. 3 represents one of the reacting 
wheels placed upon a vertical shaft, 
with the cistern by which it is supplied 
with water; to this is also attached 
what is denominated the lighter , which 
is intended to relieve the lower gudgeon 
and step from the pressure of the co¬ 
lumn of water, and also, when desired, 
the weight of the wheel, and whatever 
is attached thereto. The whole being shown in a ver¬ 
tical section through the axis of the wheel. 

“A A is the cistern of water, the construction of 
which, with its penstock, may be seen at B A, fig. 4. 

“ D the wheel, the flancli on its upper side, passing 
within the edge of that on the lower plate of the cistern. 

“ L L the lighter for relieving the gudgeon and step of 
the shaft and wheel from the downward pressure. 


Figure 3. 





























396 


APPENDIX. 


“The lighter is a circular plate of iron, concentric 
with the wheel, and attached to the same shaft. Upon 
its lower side is a flancli or projecting rim, fitting into 
an orifice in the upper plate of the cistern, in the same 
manner in which that of the wheel fits into the lower 
plate; allowing, therefore, of a vertical motion of the 
shaft to a certain extent, without binding upon the 
plates of the cistern. 

“From the equal pressure of fluids in all directions, 
the lighter, (when equal in its area to that of the orifice 
of the wheel,) will be pressed upwards with the same 
degree of force with which the latter, (the wheel,) is 
pressed downwards; and if made larger, it will be 
pressed upwards with a greater force; and may be so 
proportioned as to take off the weight both of the ma¬ 
chinery and of the water, from the gudgeon and its step. 

“ When a single wheel is placed upon a horizontal 
shaft, the lighter will take the place of the second wheel, 
and so also in the case of any odd number of wheels, 
either on a vertical or horizontal shaft. 

“ Fig. 4 represents the Figure 4. 

double reacting wheel on 
a vertical shaft. A being 
the penstock—B the cis¬ 
tern—D D the wheels, re¬ 
volving within the plates 
of the cistern in the same 
manner as the wheel and 
lighter in fig. 3. 

“ The upper wheel in 
this arrangement answers 
all the purposes of the 
lighter in the former, the 
orifice of which may be enlarged, if desired, with the 
same views.” 

The foregoing is a description of the reaction wheel, 
as patented by Mr. Calvin Wing, and is given in the lan¬ 
guage of his specification; it exhibits, therefore, his views 
upon the subject. The buckets are sometimes so made as 
not to lap, the inner end of one terminating in a line with 
the outer end of another. Some persons construct them 
































































APPENDIX. 


397 


so that the buckets are adjustable, thus allowing the 
apertures to be enlarged or diminished, according to the 
quantity of water employed, or of machinery to be 
driven. There are, in fact, not fewer, we believe, than 
eight or ten patents for different modifications of this 
wheel, and from the interest which it has excited, it 
may be considered as in a fair way to have its relative 
merits fully tested. 













EXPLANATION, ETC. 


399 


Explanation of the Technical Terms , d*c., used in the Work. 

Aperture —The opening by which water issues. 

Area —Plane, surface, superficial contents. 

Algebraic signs used are : -f for more, or addition; — less, subtracted; 
X multiplication; -r- division; = equality; the square root of; 
86 3 for 86 squared; 88 3 for 88 cubed. 

Biquadrate —A number squared, and the square multiplied into itself 
—the biquadrate of 2 is 16. 

Corollary —Inference. 

Cuboch —A name for the unit or integer of a power, being the effect 
produced by one cubic foot of water in one foot perpendicular de¬ 
scent. 

Cubic foot of water —What a vessel one foot square and one foot deep 
will hold. 

Cube of number —The product of a number multiplied by itself twice. 

Cube root of a number —say of 8;—the number which multiplied into 
itself twice will produce 8; namely 2. Or, it is that number by 
which, if you divide a number twice, the quotient will be equal to 
itself. 

Decimal point —set at the left hand of a figure, shows the whole num¬ 
ber to be divided into tens, as, .5, for y^-ths; .57 for froths; .557 for 

i¥oV tlls P arts - 

Equilibrio , Equilibrium —Equipoise or balance of weight. 

Elastic —Springy. 

Friction —The act of rubbing together. 

Gravity —The tendency all matter has to fall downwards. 

Hydrostatics —The science which treats of the weight of fluids. 

Hydraulics —The science which treats of the motion of fluids, as in 
pumps, water-works, &c. 

Impulse —Force communicated by stroke, or other power. 

Impetus —Violent effort of a body inclining to move. 

Momentum —The force of a body in motion. 

Maximum —Greatest possible. 

Non-elastic —Without spring. 

Octuple —Eight times told. 

Paradox —Contrary to received opinion; an apparent contradiction. 

Percussion —Striking together, impact. 

Problem —A question proposed. 

Quadruple —Four times, fourfold. 




400 


EXPLANATION, ETC. 


Radius —Half the diameter of a circle. 

Right angle —A line square, or perpendicular to another. 

Squared —Multiplied into itself; 2 squared is 4. 

Theory —Speculative plan existing only in the mind. 

Tangent —A line perpendicular to, or square with, a radius, and touch¬ 
ing the periphery of a circle. 

Theorem —Position laid down as an acknowledged truth. A rule. 
Velocity —Swiftness of motion. 

Virtual or effective descent of water —(See Article 61.) 


SCALE FROM WHICH THE FIGURES ARE DRAWN IN 
THE PLATES FROM II. TO XI. 

Plate II. Fig. 11, 12, 8 feet to an inch; fig. 19, 10 feet to an inch. 

III. Fig. 19, 20, 23, 26, 10 feet to an inch. 

IV. Fig. 28, 29, 30, 31, 32, 33, 10 feet to an inch. 

VI. Fig. 1, 10 feet to an inch; fig. 2, 3, 8, 9, 10, 11, 2 feet to 
an inch. 

VII. Fig. 12, 13, 14, 15, 2 feet to an inch; fig. 16, 10 feet to 
an inch. 

X. Fig. 1, 2, 18 feet to an inch; fig. H. I, in fig. 1, 4 feet to 
an inch. 

XT. Fig. 1, 2, 3, 2 feet to an inch; fig. 6, 8, 1 foot to an inch. 


THE END 







Plate 1. 

























































































Ph.1i*. II . 
















































































































































































































































































































































































































































































































































































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Hate XX1\ 
















































































































































































































































































































































































































































































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PI i. XXVII 


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BLANCHARD & LEA’S CATALOGUE 

OF 

EDUCATIONAL AND MISCELLANEOUS 

PUBLICATIONS. 


In presenting the following Catalogue, the publishers would remark that they will 
at all times take pleasure in answering inquiries relative to their publications, and 
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A .NEW TEXT-BOOK ON ANCIENT HISTORY—(Now Ready.) 


A MANUAL OF ANCIENT HISTORY, 

FROM THE REMOTEST TIMES TO THE OVERTHROW OF THE 

WESTERN EMPIRE, A. D. 476. 


BY Dr. LEONHARD SCHMITZ, F. R. S.E., 

RECTOR OF THE HIGH SCHOOL OF EDINBURGH. 


With Copious Chronological Tables. 


Ill one handsome royal 12mo. volume of four hundred and sixty-six pages, extra cloth. $1 00. 


The object of the author has been to supply the want of a clear and compendious resume of An¬ 
cient History, exhibiting within a moderate compass the annals of the Asiatic and African, as well 
as of the Classical Nations, as elucidated by the investigations of modern explorers and critics. 
The vast body of new information which has been accumulated of late years has thrown a new 
IjVht over many important periods, and renders a work like the present of much importance to 
the scholar and' private reader, as well as admirably adapted for use in colleges and academies. 
Availin' 1- himself of the successful labors of the more recent investigators, the author has not con¬ 
fined himself to the dry details of battles and sieges, but has endeavored throughout to give a clear 
and accurate description of the social and political condition of the various nations, tracing the 
progress of their civilization, the causes of their successive preponderance, the influences which 
thev have exerted, and the reasons of their decline. The name of the author is sullicient guaran¬ 
tee of the accuracy of the work, while the philosophic and democratic spirit which pervades it, 
and the .easy and perspicuous flow of its narration, cannot fail to render it a favourite with those 

for whom it is intended. 


The history is constructed with art, and every lead¬ 
ing event is surrounded with such accessaries as will 
place it« importance clearly before the mind. 1 ne 
difficulty, rarely overcome by compilers of manuals, 
i* to present a broad historical view uniformly over 
a Vast space of time, and including many nations and 
systems, and to reconcile the introduction of charac¬ 
teristic details with the general proportions of the 
narrative. Dr. Schmitz has happily surmounted 
these hardships of his task, and has produced a full 
and masterly survey of ancient history. His manual 
is one of the best that can be placed in the student s 
hands.— Athenaeum , June 20, lto5. 

The work is all that, and more than, he represents 
it to be We have closely examined such portions 
of the history as we are best acquainted with, and 
have been unable to detect a single error ot tact. 
The general accuracy of the work, therefore, seems 
to us S unimpeachable, while Hie diction t« concise, 
£cid, fluent, and vigorous. The chronological table 
appended is comprehensive and well arranged, and 
?he minute index added to this renders the volume 
one of the most valuable historical works of reteruice 
ever printed. We shall be surprised it it does not 


become a popular text-book in our high schools and 
colleges, as well as a favorite volume with intelligent 
general readers.— N. Y. Commercial Advertiser. 

From Prof. J. T. Champlin. Watervllle College. Me.. 
July 10, 1855. 

I have no hesitation in saying that it is by far the 
best manual of Ancient History with which l am ac¬ 
quainted. The introduction of the history of the non- 
classical nations is an entirely new and important 
feature, and with the greater completeness of the 
chronological tables and the general excellence of 
the whole, cannot fail to commend it to public favor. 
I shall recommend it to my classes with pleasure. 

From IV. J. Clarice, Esq, Georgetown, D. C., 
June 13, 1855. 

One of the best compends of Ancient History with 
which 1 am familiar. The most philosophical in iis 
arrangement, it combines most admirably ihe two ele¬ 
ments most difficult 10 unite—concisent ss and fulness. 
I shall substitute it for the work at present used in my 
classes, 10 which 1 give it an immense preference. 





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, WITH NOTES AND A GLOSSARY, 

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The subject of Physical Geography is one of which the acknowledged importance is rapidly 
forcing its introduction into all systems of education which pretend to keep themselves on a level 
w ith the improvements and requirements of the age. It is nodonger considered sufficient to drill 
the scholar into a mechanical knowledge of the names of rivers and mountains, and the territorial 
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who in the present volume has set forth, in a picturesque and vivid style, a popular yet condensed 
account of the globe, in its relations with the Solar System ; its geological forces ; its configuration 
and divisions into land and water, mountain, plain, river, and lake ; its meteorology, mineral pro¬ 
ductions, vegetation, and animal life ; estimating and analyzing the causes at work, and their 
influence on plants, animals, and mankind. A study such as this, taken in conjunction with 
ordinary political geography, lends to the latter an interest foreign to the mere catalogue of names 
and boundaries, and, in addition to the vast amount of important information imparted, tends to 
impress the whole more strongly on the mind of the student. 

Eulogy is unnecessary with regard to a work like the present, which has passed through three 
editions on each side of the Atlantic within the space of a few years. The publishers therefore 
only consider it necessary to state that the last London edition received a thorough revision at the 
hands of the author, who introduced whatever improvements and corrections the advance of sci¬ 
ence rendered desirable ; and that the present issue, in addition to this, has had a careful examina¬ 
tion on the part of the editor, to adapt it more especially to this country. Great care has been 
exercised in both the text and the glossary to obtain the accuracy so essential to a work of this 
nature ; and in its present improved and enlarged state, with no corresponding increase of price, 
it is confidently presented as in every way worthy a continuation of the striking favor with which 
it has been everywhere received. 


From Lieutenant Maury, U. S. N. 

National Observatory, Washington. 

I thank you for the “Physical Geography;” it is J 
capital. I have been reading it, and like it so much ! 
that I have made it a school-book for my children, 
whom I am teaching. There is, in my opinion, no 
work upon that interesting subject on which it treats— 
Physical Geography—that would make a better text¬ 
book in our schools and colleges. I hope it will be 
adopted as such generally, for you have American' 
tzed it and improved it in other respects. 


From Samuel II. Taylor, Esq, Philips Academy, 
Andover, Mass., Feb. 15, lc54. 

We have introduced your edition of Mrs. Somer¬ 
ville’s “Physical Geography” into our school, and 
find it an admirable work. 

From Thomas Shertvin, High School, Boston. 

I hold it in the highest estimation, and am confident 
that it will prove a very efficient aid in the education 
of the young, and a source of much interest and in- 
| struction to the adult reader. 


A NEW CLASSICAL ATLAS—(Nearly Ready.) 

AN xVTLAS OF CLASSICAL GEOGRAPHY. 

Constructed by WILLIAM HUGHES, and Edited by GEORGE LONG. 
WITH AN INDEX OF PLACES. 

Revised, with additional Maps and a Geographical Introduction, 

BY THE AMERICAN EDITOR. 

WITH TWENTY-SIX COLORED MAPS, LARGE IMPERIAL QUARTO, 

In one very handsome imperial octavo volume, strongly half bound. 

The name of Mr. Long as a sound and accurate classical scholar is too well known to render 
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In re-producing it in this country, some additions have been thought desirable, to render it in every 
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where they had been omitted. With these advantages, the work is therefore presented with con¬ 
fidence as in every respect calculated lo meet the want of a well-executed, accurate, and complete 
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About two thousand pages, and nearly one thousand Illustrations on Steel and Wood. 


To accommodate those who desire separate treatises on the leading departments of Natural 
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Part I. Mechanics. Part III. Optics. 

Part II. Hydrostatics, Hydraulics, Pneumatics, and Sound. 

It will thus be seen that this work furnishes either a complete course of instruction on these 
subjects, or separate treatises on all the different branches of Physical Science. 

The object of the author has been to prepare a work suited equally for the collegiate, acade¬ 
mical, and private student, who may desire to acquaint himself with the present state of science, 
in its most advanced condition, without pursuing it through its mathematical consequences and 
details. Great industry has been manifested throughout the work to elucidate the principles ad¬ 
vanced by their practical applications to the wants and purposes of civilized life, a task to which 
Dr. Lardner’s immense and varied knowledge, and his singular felicity and clearness of illustra¬ 
tion render him admirably fitted. This peculiarity of the work recommends it especially as the 
text-book for a practical age nnd country such as ours, as it interests the student’s mind by show¬ 
ing him the utility of his studies, while it directs his attention to the further extension of that 
utility by the fulness of its examples. Its extensive adoption in many of our most distinguished 
colleges and seminaries is sufficient proof of the skill with which the author’s intentions have been 
carried out. 


From Prof. Kirkwood, Delaware College, April 12,1851.1 

After a careful examination, I am prepared lo say 
that it is the most complete “Handbook of Astrono¬ 
my” with which I am acquainted. I trust the demand 
for the work will be commensurate whh its merits. 


panion for his First and Second Course. It is won¬ 
derfully minute, and yet not prolix. The principles 
of Astronomy are probably as clearly defined and 
judiciously arranged in this book as they can be. I 
expect to introduce it in my school. 


From Prof. A. Caswell. Brown University, 

April 29, 1854. 

1 regard it as a very useful and very convenient 
popular compend of ilie sciences of which it treats, 
it is full of information and well illustrated. It de¬ 
serves a place among the best educational treatises 
on Astronomy and Physics. 

From Prof. W. L. Brown. Oakland College, Miss., 
March 29, 1854. 

I consider them most admirably suited for the pur 
noses designed by the author—indeed, as the very 
best normlar works on physical science with which 
1 am acquainted. The ‘ Third Course” on Astrono¬ 
my. is especially valuable; its magnificent engrav¬ 
ings and lucid explanations make it a most desira¬ 
ble text-book. 

From Prof R. Z. Mason, McKendree College. III. 

In my judgment it contains the best selection of 
compact demonstrations and popular illustrations that 
we have yet received on the subject. Dr. Lardner 
has relieved it somewhat from the dry details of 
Mathematics, and yet there is such a close adherence 
io severe methods of thought as to satisfy the most 
rigid and careful analyst. 

From Rev. J G. Ralston, Norristown , Pa., 

M arch 22, 1854. 

Lardner’s Meteorology and Astronomy is a fit com¬ 


From S. Schooler, Esq., Hmover Academy, Ya., 
April Id, 1»54. 

The three volumes constitute a body of information 
and deiail on nearly the whole range of physical 
science which is not to be found together in any other 
publication with which I am acquainted. I hope 
that these works may be the means of inducing 
many of our youth to devote themselves to the de¬ 
velopment of the Lawsof Nature, and the applicaiion 
of them to indusry, and that they may be the vehicle 
for conveying sound information and food for thought 
to every man who aspires to be well educated. 

From M. Conant, State Normal School, Mass , 
April 11, 1854. 

This is a treatise admirably adapted to its purpose. 
For the accurate knowledge it unfolds, and the very 
popular dress it appears in, I think I have met wnh 
nothing like it. I si all advise the students of the 
Normal School to add this to your edition of Lard- 
ner's Mechanics, &c. 

From Prof. E. Everett, New Orleans, Feb. 25, 1854. 

I am already acquainted with the merits of this 
hook, having had occasion to consult it in teaching 
the branches of which it treats, and I cannot give you 
a stronger assurance of my high opinion of it than the 
simple fact that 1 have selected it as the text book of 
Physics in the course of study which I have just fixed 
upon for a new college to be established here. 









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A COMPLETE COURSE OP NATURAL SCIENCE—(Just Issued.) 


THE BOOK 



NATURE; 


AN ELEMENTARY INTRODUCTION TO THE SCIENCES OF 

Physics, Astronomy, Chemistry, Mineralogy, Geology, Botany, Zoology, and Physiology. 
BY FREDERICK SCIIOEDLER, Ph. D., 

Professor of the Natural Sciences at Worms. 


FIRST AMERICAN EDITION, 

Witli a Glossary, and oilier Additions and Improvements. 

FROM TUE SECOND ENGLISH EDITION, TRANSLATED FROM THE SIXTH GERMAN EDITION, 

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ILLUSTRATED BY SIX HUNDRED AND SEVENTY-NINE ENGRAVINGS ON WOOD. 

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The necessity of some acquaintance with the Natural Sciences is now so universally admitted in 
all thorough education, while the circle of facts and principles embraced in the study has enlarged 
so rapidly, that a compendious Manual like the Book of Nature cannot fail to supply a want fre¬ 
quently felt and expressed by a large and growing class. 


Composed by the same distinguished author, all the 
departments have a uniformity of style and illustra¬ 
tion winch harmoniously link the entire circle to¬ 
gether. The utility of such a connected view of the 
physical sciences, and on such an approved basis, is 
beyond price; and places their acquisition within 
ihe reach of a vastly increased number of inquirers. 
Not only to such is it valuable, but to those who wish 
to have at hand the means of refreshing their memo¬ 
ries and enlarging their views upon their favorite 
studies. Of such a book we speak cordially, and 
would speak more at length. if space permitted.— 
Southern Methodist Quarterly Review. 

FromlV. H Allen, President of Girard College, Philada. 

Though a very comprehensive book, it contains 
about as much of the details of natural science as 
general students in this country have time to study in 
a regular academical course; and I am so well 
pleased with it that 1 shall recommend its use as a 
text-book in this institution. 


From Prof. Johnston. Wesleyan University, Ct., 
March 14. 1854. 

I do not know of another hook in which so much 
that is important on these subjects can be found in 
the same space. 

From Prof. Allen, Oberlin Institute, Ohio, April 1,1S54. 

As a work for popular instruction in the Natural', 
and Physical Sciences, it certainly is unrivalled, so 
far as my knowledge extends. It admirably com¬ 
bines perspicuity with brevity; while an excellent 
judgment and a rare discrimination are manifest in 
the selection and arrangement of topics, as well as m 
the description of objects, the illustration of pheno¬ 
mena. and the statement of principles. A more care¬ 
ful perusal of those departments of the work to which 
my studies have been particularly directed has been 
abundantly sufficient to satisfy me of its entire reli¬ 
ableness—that the object of the author was not so 
J much to amuse as really to instruct. 


TEXT-BOOK OF SCRIPTURE GEOGRAPHY AND HISTORY—(Just Issued.) 


OUTLINES OF SCRIPTURE GEOGRAPHY AND HISTORY; 

Illustrating the Historical Portions of the Old and New Testaments. 

DESIGNED FOR THE USE OF SCHOOLS AND PRIVATE READING. 

BY EDWARD HUGHES, F.R.A.S., F.G.S., 

Head Master of the Royal Naval Lower School, Greenwich. &c. 
based upon coleman’s historical geography of tiie bible. 

With twelve handsome colored Maps. 


In one very neat royal 12mo. 

TVe have given it considerable examination, and 
have been very favorably impressed with it as a 
worn of rare excellence, and as well calculated to 
answer a demand, which, so far as our knowledge 
extends, has never yet been fully accomplished.— 
Evangelical Repository. 

A concise and very convenient condei sation of 
just such facts and information as the Biblical student 
and general reader want always at hand. We com¬ 
mend it without reserve.— N. Y. Recorder. 

We have rend it with care, and can recommend it 
with confidence. Indeed, we do not know of a more : 
convenient and reliable handbook fora pastor, Sun¬ 
day-school teacher, or a general student to refer to 
for information in regard to Palestine, whether as to 
its physical features or its geography, its climate or 
its productions, its past history or its present condi- ; 
lion —Southern Presbyterian. 

From ProfSamuel II. Turner , N. Y. Theological 
Seminary. 

It appears to contain in a compressed form a vast 
deal of important and accurate geographical and 
historical information I hope the book will have the 
wide circulation which its merits entitle it to. I shall 
not fail to recommend it so far as opportunity offers. 


volume, extra cloth. $1 00. 

From Rev. Eliphalel Nott, President of Union College, 
N. l r ., Feb. 2U, 1854. 

Few more interesting class books where the Bib'e 
is used in schools can be found than the “Outlines of 
Scripture Geography and History.” and it will prove, 
in families where the Bible is read, a valuable aux¬ 
iliary to the understanding of that blessed volume. It 
is therefore to be hoped that it will receive that patro¬ 
nage which it so richly deserves. 

From Rev. Samuel Findley, President of Antrim 
College , Ohio, Feb. 18,1^54. 

We have long needed just such a book, and as soon 
as possible we shall make it one of the text books of 
our college. It should be a text-book in all our 
theological institutions. 

From Prof. E. Everett , New Orleans, Feb. 25,1854. 

I have studied the greater portion of it with care, 
and find it so useful as a book of reference that I have 
placed it on the tabic with my Bitde as an aid to my 
daily Scripture readings. It is a book which ought 
to he in the hahds of every biblical student, and 1 can¬ 
not but hope that it will have a wide circulation. To 
such as desire to borrow I answer, “I cannot loan it, 
lor I am obliged to refer to it daily 1” 






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5 


NOW COMPLETE. 

SCHMITZ & ZUMPT’S” CLASSICAL SERIES. 

The publishers have much pleasure in announcing the conclusion of this Series, which now- 
presents a set of class-books sufficient for a complete course of study in the Latin language. The 
very numerous recommendations which it has received from classical scholars and practical 
teachers, and its extensive introduction into many of our best seminaries and colleges, show that 
the objects of the distinguished editors have been fully carried out in its preparation. These objects 
have been to present a uniform set of text-books, based upon the most approved systems of modern 
education, conducting the student from the commencement of his studies to their conclusion on 
one definite plan, thus relieving the teacher from the annoyance of passing progressively through 
works based upon different and conflicting systems; a choice selection of classical authors has 
been made, which are printed from the most correct and approved texts, and are accompanied 
with biographical and critical notices, illustrations, and maps wherever necessary, and explanatory 
notes introduced sparingly, affording assistance where it is required, without overburdening the 
author with commentary. 

In the typographical execution of the works everything has been done to adapt them to the 
wants of the teacher and student. Printed uniformly in a handsome royal 18mo. form, they are 
convenient for use, while at the same time the prices at which they are offered are unprecedentedly 
low. Every care has been taken to secure the verbal and literal accuracy so necessary in educa¬ 
tional works, while most of the volumes can be had in neat extra cloth, or strongly half bound, 
with leather backs and cloth sides. 

^The Series consists of the following works: — 

SCHMITZ’S ELEMENTARY LATIN GRAMMAR. To which is added a SERIES OF EXER¬ 
CISES FOR PARSING AND TRANSLATION; with Vocabularies and Notes. Price 50cents 
in cloth; half bound, 55 cents. 

SCHMITZ’S ADVANCED GRAMMAR OF THE LATIN LANGUAGE. Half bound, price 
60 cents. 

ADVANCED LATIN EXERCISES, WITH SELECTIONS FOR READING. Revised, with 
Additions. Extra cloth, price 50 cents; half bound, 55 cents. (Now ready.) 

This work is complete in itself, containing all the Rules of Syntax — Explanatory Notes 
Directions for the Position of Words, &c. &c. 

KALTSCHMIDT’S SCHOOL DICTIONARY OF THE LATIN LANGUAGE. In two parts, 
Latin-English, and English-Latin. Complete in one very thick volume, of nearly 900 double- 
columned pages, full bound in strong leather. Price $1 30. 

Also, Part I, Latin-English, sold separate, full bound. Price 00 cents. 

Part II, English-Latin, sold separate, full bound. Price 75 cents. 

CORNELII NEPOTIS LIBER DE EXCELLENTIBUS DUCIBUS Exterarum Gentium, cum 
Vitis Catonis et Attici. With Notes, &c. Price in extra cloth, 50 cents; half bound, 55 cts. 

C. I. CiESARIS COMMENTARII DE BELLO GALLICO. With Notes, Map, and other illus¬ 
trations. Price in extra cloth, 50 cents; half bound, 55 cents. 

C. C. SALLUSTII DE BELLO CATILINARIO ET JUGURTHINO. With Notes, Map, &c. 
Price in extra cloth, 50 cents; half bound, 55 cents. 

EXCERPTA EX P. OVIDII NASONIS CARMINIBUS. With Notes, &c. Price i a extra cloth 
60 cents ; half bound, 65 cents. 

Q. CURTII RUFI DE GESTIS ALEXANDRI MAGNI LIBRI VIII. With Notes, Map, &c. 
Price in extra cloth, 70 cents; half bound, 75 cents. 

P. VIRGILII MARONIS CARMINA OMNIA. Price in extra cloth, 75 cents; half bound, SO cts. 

T. LIVII PATAVINI HISTORIARUM, LIBRI I.. II., XXI., XXII. With Notes, two colored 
Maps, &c. Price in extra cloth, 70 cents; half bound, 75 cents. 

M T CICERONIS ORATIONES SELECTEE XII. W T ith Notes, &c. Price in extra cloth, 60 
cents; half bound, 65 cents. 

ECLOG/E EX Q. IIORATII FLACCI POEMATIBUS. With Notes, &c. Price in extra cloth, 
60 cents; half bound, 65 cents. 

In its complete state, it will thus be seen that this Series presents a thorough and uniform 
course of instruction in Latin, from the rudiments to the lower collegiate classes. 

From among many hundred recommendatory notices with which they have been favored, the 
publishers append a few. 

From Prof. W. 11. Doherty, Antioch College, Ohio. 

I greatly admire the beautiful and most useful se¬ 
ries of Latin authors which you*have published. [ 
regard them as a real boon to ull students of moderate 
means, they are so cheap, so comprehensive, and so 
correct. They constitute, in fact, an admirable course 
of Latin reading, and their wonderful cheapness 
places them wi hilt the reach of the humblest and 
poorest student. 


From Prof. N. W. Benedict , Rochester University, N. Y. 

I have taken pains to examine the works and am 
happy to find them very superior for the purposes 
designed. The selection made from Latin authors is 
a judicious one; the editorial labor is of the right 
kiid and the mechanical execution of the works, 
totrether with the low price at which they are afford- 
^ constitute them a valuable aid towards the fur¬ 
therance of classical studies m this country. 







G 


ELAN CHARD & LEA’S EDUCATIONAL PUBLICATIONS. 


SCHMITZ & ZTJMPT’S CLASSICAL SERIES—(Continued.) 


From Prof. J. J. Owen. N. Y. Free Academy. 

With your classical series I nm well acquainted 
and have no hesitancy in recommending them to all 
my friends In addition to your Virgil, which we use, 
we shall probably adopt other hook* of the series as 
we may have occasion to introduce them. 

From Reginald II Chase , Harvard University , Mass. 

I have taken time to give the two Grammars a par¬ 
ticularly careful examination, and I was not surprised 
to find them equally admirable in plan and execution 
with the other works of your series. They are pre¬ 
cisely what l have been longing for. My pupils have 
provided themselves with them, and they will here¬ 
after. in common with the other volumes of the series, 
)>e required as text-books with all my scholars. In 
our Latin school no others will be allowed. 

From Prof. A Rollins, Delaware College. 

I regard this series of Latin text books as decidedly 
superior to any others with which I am acquainted. 
The Livy and Horace I shall immediately introduce 
for the use of the college classes. 

From Prof. A. C Knox , Hanover College, Ind. 

Having examined several of them with some de¬ 
gree of care, we have no hesitation in pronouncing 
them among the very best extant. 

From Prof. R. N. Newell, Masonic College, Tenn. 

1 tan give you no better proof of the value which 
I set on ihem than by making use of them in my own 
classes, and recommending tbeir use in the prepara 
lory department of our institution. I have read them 
through carefully that I might not speak of them with¬ 
out due examination, and 1 flatter myself that my 
opinion is fully borne out by fact, when I pronounce 


them to be the most useful and the most correct, as 
well as the cheapest editions of Latin Classics over 
introduced in this country. The Latin and English 
Dictionary contains as much as the student can want 
in the earlier years of his course; it contains more 
than I have ever seen compressed into a hook of this 
kind. It ought to be the student’s constant companion 
in his recitations. It has the extraordinary recom¬ 
mendation of being at once portable and comprehen¬ 
sive. 

Among the various editions of the Latin Classics, 
Schmitz and Zumpt’s series, so far as yet published, 
are at all times preferred, and students are requested 
10 procure no oilier.— Announcement of Bethany Col¬ 
lege, Va. 

But we cannot forbear commending especially, 
both to instructors and pupils, the whole of the series 
edited by those accomplished scholars, l>r«. Schmitz 
and Zurnpt. Here will be found a set of text-books 
that combine the excellences so long desired in this 
class of works. They will not cost ihe student, by 
one-half at least, that which he must expend for some 
other editions. And who will not say that this is a 
consideration worthy of attention? For the cheaper 
our school-books can be made, the more widely will 
they he circulated and used. Here you will find, too, 
no useless display of notes and of learning, but in 
foot-notes on each page yon have every thing neces¬ 
sary to the understanding of the text. The difficult 
points are sometimes elucidated, and often is the stu¬ 
dent referred to the places where he can find light, 
but not without some effort of his own. We think 
that the punctuation in these books might be im¬ 
proved; but taken as a whole, they'come nearer to 
the wanls of the times than any within our know¬ 
ledge.— Southern College Review. 


UNIFORM WITH SCHMITZ & ZUMPT'S CLASSICAL SERIES. 


BAIRD’S CLASSICAL MANUAL. 


THE CLASSICAL MANUAL; an Epitome of Ancient Geography, Greek ani> 
Roman Mythology, Antiquities, and Chronology. Chiefly intended for the use 
of Schools. By the Rev. James S. S. Baird, T.C.D., Assistant Classical Master, 
King's School, Gloucester. In one neat royal 12mo. volume. Price in extra cloth, 
50 cents ; half bound, 55 cents. 


This little volume has been prepared to meet the recognized want of an Epitome which, within 
the compass of a single small volume, should contain the information requisite to elucidate the 
Greek and Roman authors most commonly read in our schools. The aim of the author has been 
to embody in it such details as are important or necessary for the junior student, in a form and 
space capable of rendering them easily mastered and retained ; and he has consequently not incum¬ 
bered it with a mass of learning which, though highly valuable to the advanced student, is merely 
perplexing to the beginner. In the amount of information presented, and the manner in which 
it is conveyed, as well as its convenient size and exceedingly low price, it is therefore admirably 
adapted for the younger classes of our numerous classical schools. 

Although issued but very recently, this little work has commanded universal approbation ; and 
its immediate introduction into a large number of our best educational institutions, sufficiently 
proves that the author has succeeded in filling a vacancy among our classical text-books. 


From Prof. J. S. Hart. Principal of the Philadelphia 
High School. 

‘ Baird’s Classical Manual” is an admirable com- 
pend of the knowledge most indispensable to the stu¬ 
dent of Greek and Roman antiquities. 

From Prof P. B. Spear , Madison University, N. Y. 

I atn persuaded, from the examination which 11 ave 
given it, that if a class were to be drilled upon such 
an ‘ Epitome” as this, nothing better would lay a 
foundation for a full and accurate knowledge of the 
Geography. Chronology, Mythology, and Antiquities 
of the Greeks and Romans. 


From Prof. R. W. Newell, Masonic College, Tenn. 

I cannot help thinking that in none of your works 
have you so effectually provided for the wants of toe 
poor student us in this. 

From Reginald II. Chase , Harvard University. 

That invaluable little work, the Classical Manual, 
has been used by me for some time. I would not on 
Mty account be without it. You have not perhaps 
been informed that it has recently been introduced in 
the High School of this place. Its typographical ac¬ 
curacy is remarkable. 


ARNOT’S ELEMENTS OF PHYSICS. 

ELEMENTS *0F PHYSICS; OR, NATlRAlTpiHLOSOPHY, GENERAL AND MEDICAL. 

Written for Universal Use in Plain or Non-Technical Language. 

BY NEILL ARNOT, M. D. 

In one octavo volume, leather, with about two hundred illustrations. $2 50. 













BLANCHARD & LEA’S EDUCATIONAL PUBLICATIONS. 


7 


BOLBIAR’S COMPLETE FRENCH SERIES. 

Blanchard & Lea now publish the whole of Bolmar’s Educational Works, forming a complete 
series for the acquisition of the French language, as follows: — 

BOLMAR’S EDITION OF LEVIZAC’S THEORETICAL AND PRACTICAL GRAMMAR OF 
THE FRENCH LANGUAGE. With numerous Corrections and Improvements, and the addi¬ 
tion of a complete Treatise on the Genders of French Nouns and the Conjugation of the French 
\ erbs, Regular and Irregular. Thirty-fifth edition. In one 12mo. volume, leather, Si 00. 

BOLMAR'S COLLECTION OF COLLOQUIAL PHRASES, on every topic necessary to main¬ 
tain conversation; arranged under different heads; with numerous remarks on the peculiar 
pronunciation and use of various words. The whole so disposed as considerably to facilitate the 
acquisition of a correct pronunciation of the French. In one 18mo. volume, half bound, 37^ cts. 

BOLMAR’S EDITION OF FENELON’S AVENTURES DE TELEMAQUE. In one 12mo. 
volume, half bound, 55 cents. 

BOLMAR’S KEY TO THE FIRST EIGHT BOOKS OF TELEMAQUE, for the literal and 
free translation of French into English. In one 12mo. volume, half bound, 55 cents. 

BOLMAR’S SELECTION OF ONE HUNDRED OF PERRIN’S FABLES, accompanied with a 
Key, containing the text and a literal and a free translation, arranged in such a manner as to 
point out the difference between the French and the English Idiom; also, a figured pronuncia¬ 
tion of the French. The whole preceded by a short treatise on the Sounds of the French lan¬ 
guage as compared with those of English. In one ]2mo. volume, half bound, 75 cents. 

BOLMAR’S BOOK OF FRENCH VERBS, wherein the Model Verbs, and several of the most 
difficult, are conjugated Affirmatively, Negatively, Interrogatively, and Negatively and Inter¬ 
rogatively, containing also numerous Notes and Directions on the Different Conjugations, not to 
be found in any other book published for the use of English scholars; to which is added a com¬ 
plete list of all the Irregular Verbs. In one 12mo. volume, half bound, 50 cents. 

The long and extended sale with which these works have been favored, and the constantly in¬ 
creasing demand which exists for them, renders unnecessary any explanation or recommendation 
of their merits. The fact that 

Over two hundred thousand volumes 

have been sold is the best evidence that their long-continued popularity is founded on their intrinsic 
merit and skilful adaptation to the wants of the student and teacher. 


BUTLER’S ANCIENT ATLAS. 

AN ATLAS OF ANCIENT GEOGRAPHY. 

BY SAMUEL BUTLER, D. D., 

Late Lord Bishop of Litchfield. 

In one handsome octavo volume, half bound, containing twenty-one colored M?ps, and an 

Accentuated Index. $1 50. 

The very low price at which this work is now offered, and the authoritative position which it 
has so long maintained, render it a very desirable reference book for all institutions where this 
branch of study is pursued. Used in conjunction with the following volume, it forms a complete 
course of classical geography. 

BUTLER’S ANCIENT GEOGRAPHY. 

GEOGRAPHIA CLASSICA; 

OR THE APPLICATION OF ANCIENT GEOGRAPHY TO THE CLASSICS. 

BY SAMUEL BUTLER, D. D., 

Late Lord Bishop of Litchfield. 

Sixth American, from the last ami revised London Edition. 

With Questions on the Maps, by JOHN FROST, LL. D., &c. 

In one neat volume, royal 12mo., half bound, 75 cents. 


MULLER’S PHYSICS. 

PRINCIPLES OF PHYSICS AND METEOROLOGY. 

By Prof. J. MULLER. 

Edited, with Additions, by R. E. GRIFFITH, M. D. 

Tn one large and very handsome octavo volume, with 550 wood-cuts, and two colored plates. $3 50. 

it nrpscuts a systematic, minute, and comprehen- I American Editor, of articles on the Electro-Magnetic 
siieexoos fion in one middle-sized volume, of all the | Telegraph, Electrotype, Mennvengme, Sc c. The en- 
mo«t mmor atu’facts and theories relating to Statics, j graving? in this volume certain y surpass everything 
Tlvnamics, Hydrodynamics. Pueu.na- of the kind heretofore published in America. raking 
; s o f lm Motions of Waves in general, it for all in all, we know of no single work which 
<£ 8 nd the Theory of Musical Notes, the Voice and contains so satisfactory treatises on so great a num- 
t'ounu. tne ineo > .~ - -- **-—— J 1 her of subjects connected with the philosophy of na¬ 

ture— Mtihodist Quarterly Review. 


Hearing Geometrical and Physical Optics, Heat and 
Meteorology, Magnetism, Electricity and Galvanism, 
in all their subdivisions; with the addition, by the 










8 


BLANCHARD & LEA’S EDUCATIONAL PUBLICATIONS. 


SHAW’S ENGLISH LITERATURE —(Lately Published.) 


OUTLINES OF ENGLISH LITERATURE. 


BY THOMAS B. SIIAW, 

Professor of English Literature in the Imperial Alexander Lyceum, St. Petersburg. 

SECOND AMERICAN EDITION. 

WITH A SKETCH OF AMERICAN LITERATURE. 

BY HENRY T. TUCKER MAN, Esa. 

In one large and handsome volume, royal 12mo., of about five hundred pages. 

Extra cloth, $1 15 j half hound in leather, $1 25. 

The object of this work is to present to the student, within a moderate compass, a clear and 
connected view of the history and productions of English Literature. To accomplish this, the 
author has followed its course from the earliest times to the present age, seizing upon the more 
prominent “ Schools of Writing,” tracing their causes and effects, and selecting the more cele¬ 
brated authors as subjects for brief biographical and critical sketches, analyzing their best works, 
and thus presenting to the student a definite view of the development of the language and lite¬ 
rature, with succinct descriptions of those books and men of which no educated person should 
be ignorant. He has thus not only supplied the acknowledged want of a manual on this subject, 
but by the liveliness and power of his style, the thorough knowledge he displays of his topic, 
and the variety of his subjects, he has succeeded in producing a most agreeable reading-book, 
which will captivate the mind of the scholar, and relieve the monotony of drier studies. 


From Prof. J. V. Raymond, University of Rochester. 

Its merits I had not now for the first time to learn. 
I have used it for two years as a text-book, with the 
greatest satisfaction. It was a happy conception, ad¬ 
mirably executed. It is all that a text book on such 
a subject eau or need be, comprising a judicious se¬ 
lection of materials* easily yet effectively wrought. 
The author attempts just as much as he ought to, and 
does well all that he attempts; and the best of the 
hook is the genial spirit , the genuine love of genius 
and its works which thoroughly pervades it and makes 
it just what you want to put in a pupil's hands. 

From Prof. J. C. Pickard, Illinois College. 

Of“ Shaw’s English Literature” I can hardly say 
too much m praise. I hope its adoption and use as a 
text-book will correspond to its great merits. 

From Edwin Arnold, Esq., Bel-Air, Md. 

A mo«t valuable contribution to our slock of school¬ 
books. It supplies a vacuum which has been severe¬ 
ly felt by those who desired to communieaie to their 
pupils the most slender outline of belles-lettres. In 
my opinion, it is itself a most desirable work, and 
should be placed in the hands of every youth as soon 
as old enough to lay aside the tales of the nursery. 

From Prof. R. P. Bunn , Brown University. 

I had already determined to adopt it as the principal 
hook of reference in my depariment. This is the first 
form in which it has been used here; but from the trial 
which I have now made of it, I have every reason to 
congratulate myself on my selection of it as a text¬ 
book. 


From A. B. Davenport, Esq., Brooklyn N. Y. 

The work of Shaw and Tuckerman on English and 
American literature particularly interested me. it is 
iruly a rnullicm in parvo. I know not where one can 
find so much information condensed upon the topics 
on which it treats as is to be found in this work. 
Either as a text book, or for higher classes in read¬ 
ing, it is worthy of general adoption. 

From Prof. J. Munroe, Oberiin College. 

I have examined it carefully, and value it highly, 
It fills a place not occupied by any other book with 
which I am acquainted. It will probably be intro¬ 
duced in this institution as a text-book preparatory to 
the study of English literature. 

From Report of the Teachers' Association of Lauder¬ 
dale County , Ga. 

A careful perusal of the “Outlines of English Lite¬ 
rature,” by Professor Shaw, of St. Petersburg, has 
afforded us great pleasure. It is designed to place 
in the hands of the student a Manual, that, without 
being too voluminous, shall impart a general and 
correct knowledge upon a subject that ought to be 
familiar to all who use the noble old English tongue. 
By its aid, the scholar will learn how our language, 
springing from the original Saxon, by an admixture 
of Norman French, and finally of the Latin and 
Greek, has arrived at its present high state of perfec¬ 
tion. He will al-o become well acquainted with the 
most celebrated writers of England during the dif¬ 
ferent periods of her literary history, their lives, their 
characters, and their writings. We hope it will be 
extensively used. 


BROWNE’S CLASSICAL LITERATURE-(Now Complete.) 

A IIISTOEY OF GREEK CLASSICAL LITERATURE. 

By The REV. R. W. BROWNE, M.A., 

Professor of Classical Literature in King’s College, London. 

In one very handsome crown octavo volume. $1 50. 


By tlie same Autlior, to match—(Now Ready.) 

A HISTORY OF ROMAN'CLASSICAL LITERATURE. 

In one very handsome crown octavo volume. $1 50. 


From Prof. Gessner Harrison , University of Va. 

I am very favorably impressed with the work from 
what 1 have seen of it, and hope to find in it an im¬ 
portant help for my class of history. Such a work is 
very mueli needed. 

From Prof. J. A. Spencer, Neio York. 

It is an admirable volume, sufficiently full and co. 
pious in detail, clear and precise in style, very scholar- 
like in its execution, genial in its criticism, and alto- 
gether displaying a mind well stored with the learning, 
genius, wisdom, and exquisite taste of the ancient 
Greeks. It is in advance of everything we have, and 
it may be considered indispensable to tlie classical 
scholar and student. 


Mr. Browne’s present publication has great merit. 
His selection of materials is judiciously adapted to the 
purpose of conveying within a moderate compass 
some definite idea of the leading characteristics of 
the great classical authors and their works. * * * * Mr. 
Browne has the happy art of conveying information 
in a most agreeable manner. It is impossible to miss 
his meaning, or be insensible to the charms of his po¬ 
lished style. Suffice it to say, that he has, in a very 
readable volume, presented much that is useful to the 
classical reader. Besides biographical information 
in reference to all the classical Greek authors, he has 
furnished critical remarks on their intellectual pecu¬ 
liarities, and an analysis of their works when they 
are of sufficient importance to deserve it .—London 
Athenceum. 












9 


BLA NCHARD & LEA’S EDUCATIONAL PUBLICATIONS 


HERSCHEL’S ASTRONOMY. 

O U T LINES 0 F~ A S T R 0 N 0 M Y. 

B\ SIR JOHN F. W. IIERSCHEL, Bart., F. R. S., &c. 

A NEW AMERICAN, FROM THE FOURTH AND REVISED LONDON EDITION. 

In one handsome crown octavo volume, with numerous plates and wood-cuts. 

Extra cloth, $1 60 ; or, half bound, leather backs and cloth sides, $1 75. 

thJnnthI! Sen ^° rk L i8 u r u Prinl u d i from the Iast London edition, which was carefully revised by 
li rlll ’i in which he embodies the latest investigations and discoveries. It may therefore 

AY* k a ® fui, y on a level w 'th the most advanced state of the science, and even better 
adapted than its predecessors, as a full and reliable text-book for advanced classes. 

I• e '^ COI " ,n endatory notices are subjoined, from among a large number with which the pub¬ 
lishers have been favored. r 


From Professor D. Olmstead, Yale College. 

A rich mine of all that is most valuable in modern 
Astronomy. 

From Prof. A. Casivtll. Brown University. R, I. 

As a work of reference and study for the more ad¬ 
vanced pupils, who yet are not prepared to avail 
themselves of the higher mathematics, I know of no 
work to be compared with it. 

From Prof. Samuel Jones, Jefferson College , Pa., 

This treaiise is too well known, and too highly ap¬ 
preciated in the scientific world to need new praise. 
A distinguishing merit in this, as in the other produc¬ 
tions of the author, is that the language in which the 
profound reasonings of science are conveyed is so 
perspicuous that the writer’s meaning can never be 
misunderstood. 

From Prof. J. F. Crocker , Madison College, Pa, 

I know no treatise on Astronomy comparable 1o 
<£ Herschel’s Outlines.” It is admirably adapted to 
the necessities of the student. We have adopted it 
as a text-book in our College. 

From Prof. James Curley, Georgetown College, 

As far as I am able to judge, it is the best work of 
its class in any language. 

From Prof. N. Tillinghast, Bridgewater , Mass., 

It would not become me to speak of the scientific 
merits of such a work by such an author; but I may 
be allowed to say, that I most earnestly wish that it 
might supersede every book used as a text-book on 
Astronomy in all our institutions, except perhaps 
those where it is studied mathematically. 


W e now take leave of this remarkable work, which 
we hold to be, beyond a doubt, the greatest and most 
remarkable of the works in which the laws of astro¬ 
nomy and the appearance of the heavens are de¬ 
scribed to those who are not mathematicians nor 
observers, and recalled to those who are. It is the 
reward of men who can descend from the advance¬ 
ment of knowledge to care for its diffusion, that their 
works are essential to all, that they become the 
manuals of the proficient as well as the text-books of 
the learner.— Aihenceum. 

There is, perhaps, no book in the English language 
on the subject, which, whilst it contains so many of 
the facts of Astronomy (which it attempts to explain 
with as little technical language as possible), is so at¬ 
tractive in its style, and so clear and forcible in its 
illustrations.— Evangelical Review. 

Probably no book ever written upon any science, 
embraces within so small acompassan entire epitome 
of everything known within all its various depart¬ 
ments, practical, theoretical, and physical. — Ex¬ 
aminer. 

There is not, perhaps, in the English language, a 
work, treating upon so abstruse a subject, certainly 
not upon Astronomy, written with so much concise¬ 
ness and explicitness, and yet in so easy and intelli¬ 
gible a style, with such an avoidance of technicali¬ 
ties, and which one that is not an adept in the science 
can read so understandingly. The very learned au¬ 
thor has done almost as much for the cause of Astro¬ 
nomy by the preparation of this work, by wdiich the 
knowledge of it will be diffused among the people, as 
by his w'onderful discoveries.— N. Y. Observer. 


NEW PHYSIOLOGICAL TEXT-BOOK—(Now Ready.) 

PHYSIOLOGY OF ANIMA17AND VEGETABLE LIFE. 

A POPULAR TREATISE 

ON THE PHENOMENA AND FUNCTIONS OF ORGANIC LIFE. 

To which is Prefixed a Brief General View of the Great Departments of Human Knowledge. 

BY J. S. BUSHNAN, M. D. 

In one handsome royal 12mo. vol., of 234 pages, with over 100 handsome illustrations. 80 cts. 

Written by a man of Science, this work, though popular in its form and elementary in its teach¬ 
ings, avoids the objections usually urged against similar treatises, of superficiality and incorrectness. 
While its language and arrangement are such as to render it easily understood by the youthful 
student or general reader, its basis is strictly scientific, and on every point it will be found on a 
level with the most advanced state of knowledge. 


BIRD’S NATURAL PHILOSOPHY. 


ELEMENTS OF NATURAL PHILOSOPHY; being an Experimental Introduction to the Phy¬ 
sical Sciences. Illustrated with over 300 wood-cuts. By Golding Bird, M.D., Assistant 
Physician to Guy’s Hospital. From the Third London edition. In one neat volume, royal 12mo. 
extra cloth, 81 25; strong leather, $1 50. 


We are astonished to find that there is room in so 
small a book for even the bare recital of so many 
subjects. Where everything is treated succinctly, , 
great judgment and much time are needed in making j 
a selection and winnowing the wheat from the chaff, j 
Dr. Bird has no need to plead the peculiarity of 
his position as a shield against criticism, so long as 
his book continues to be the best epitome in the Eng¬ 


lish language of this wide range of physical subjects. 
—North American Review. 

From Prof. John Johnston, Wesleyan Univ., 
Middletown, Ct. 

For those desiring as extensive a work, I think it 
decidedly superior to anything of the kind with which 
I am acquainted. 













10 


BLANCHARD & LEA’S SCIENTIFIC PUBLICATIONS. 


CARPENTER’S COMPARATIVE PHYSIOLOGY. 

New and Improved Edition —Now Ready. 


PRINCIPLES OF COMPARATIVE PHYSIOLOGY. By William B. Car¬ 
penter, M. D., author of “ Principles of Human Physiology,” &c. A new American edition, 
revised and improved by the author. With over three hundred illustrations. In one large and 
very handsome octavo volume, of 750 pages. 

The delay which has existed in the appearance of this work has been caused by the very thorough 
revision and remodelling which it has undergone at the hands of the author, and the large number 
of new illustrations which have been prepared for it. 1will, therefore, be found almost a new 
work, and fully up to the day in every department of the subject, rendering it a reliable text-book 
for all students engaged in this branch of science. Every effort has been made to render its typo¬ 
graphical finish and mechanical execution worthy of its exalted reputation, and creditable to the 
mechanical arts of this country. 


This work stands without its fellow. It is one few 
men in Europe could have undertaken; it is one, no 
man, we believe, could have brought to so success¬ 
ful an issue as Dr. Carpenter. We feel that this 
abstract can give the reader a very 7 imperfect idea of 
the fulness of this work, and no idea of its unity, of 
the admirable manner in which material has been 


brought, from the most various sources, to conduce to 
its completeness, of the lucidity of the reasoning it 
contains, or of the clearness of language in which the 
whole is clothed. Not the profession only, but the 
scientific world at large, must feel deeply indebted to 
Dr. Carpenter for this great work. It must, indeed, 
add largely even to his high reputation.— Med. Times. 


CARPENTER ON THE MICROSCOPE—(Nearly Ready.) 

THE MICROSCOPE AND ITS REVELATIONS. By William B. Carpen¬ 
ter, M. D., author of “ Principles of Human Physiology,” &c. In one very handsome octavo 
volume, with several hundred illustrations. 

Various literary engagements have delayed the author’s progress with this long expected work. 
It is now, however, in an advanced state of preparation, and may be expected in a few months. 
The importance which the microscope has assumed within the last few years, as an indispensable 
assistant to all investigators in natural science, has caused the want to be severely felt of a volume 
which should serve as a guide to the learner and a book of reference to the more advanced stu¬ 
dent. This want Dr. Carpenter has endeavored to supply in the present volume. His great prac¬ 
tical familiarity with the instrument and all its uses, and his acknowledged ability as a teacher, are 
a sufficient guarantee that the work will prove in every way admirably adapted to its purpose, and 
superior to any as yet presented to the scientific world. 


JOHNSTON’S PHYSICAL ATLAS. 


THE PHYSICAL ATLAS OF NATURAL PHENOMENA. For the use of 

Colleges, Academies, and Families. By Alexander Keith Johnston, F. R. G. S., &c. In one 
large imperial 4to. volume, strongly bound in half morocco. With twenty-six plates, engraved 
and colored in the best style. Together with over one hundred pages of Descriptive Letter- 
press, and a very copious Index. Price $12 00. 


The book before us is, in short, a graphic encyclo¬ 
paedia of the sciences—an atlas of human knowledge 
done into maps. It exemplifies the truth which itex- 

L resses—that he who runs may read. The Thermal 
aws of Leslie it enunciates by a bent line running 
across a map of Europe; the abstract researches of 
Gauss it embodies in a few parallel curves winding 
over a section of the globe ; a formula of Laplace it 
melts down to a little patch of mezzotint shadow; a 
problem of the transcendental analysis, which covers 
pages with definite integrals, it makes plain to the eye 
by a little stippling and hatching on a given degree of 
longitude! All possible relations of time and space, 
heat and cold, wet and dry, frost and snow, volcano 
and storm, current and tide, plant and beast, race and 
religion, attraction and repulsion, glacier and ava¬ 


lanche, fossil and mammoth, river and mountain, 
mine and forest, air and cloud, and sea and sky—all 
in the earth and under the earth, and on the earth, 
and above the earth, that the heart of man has con¬ 
ceived or his head understood—are brought together 
by a marvellous microcosm, and planted on these 
little sheets of paper, thus making themselves clear 
to every eye. In short, we have a summary of all 
the cross-questions of Nature for twenty centuries— 
and all the answers of Nature herself set down and 

speaking to us voluminous system dans un mot . 

Mr. Johnston is well known as a geographer of great 
accuracy and research; and it is certain that this 
work will add to his reputation; for it is beautifully 
engraved, and accompanied with explanatory and 
tabular letterpress of great value.— Athenaeum. 


CHEMICAL TEXT-BOOK FOR STUDENTS—(Just Issued.) 


ELEMENTARY CHEMISTRY. Theoretical and Practical. By George 

Fownes, Ph. D., &c. With numerous illustrations. A new American, from the last and revised 
London edition. Edited, with Additions, by Robert Bridges, M. D. In one large royal 12mo. 
volume, containing over 550 pages, clearly printed on small type, with 181 illustrations on 
wood ; extra cloth, or leather. 


We know of no better text-book, especially in the 
difficultdepartment of organic chemistry, upon which 
it is particularly full and satisfactory. We would 
recommend it to preceptors as a capital “ office book” 
for their students who are beginners in Chemistry. 
It is copiously illustrated with excellent wood-cuts, 
and altogether admirably “got up.”— N. J. Medical 
Reporter, March, 1854. 

A standard manual, which has long enjoyed the 
reputation of embodying much knowledge in a small 
space. The author has achieved the difficult task of 


condensation with masterly tact. His book is con¬ 
cise without being dry, and brief without being too 
dogmatical or general.— Virginia Med. and Surgical 
Journal. 

The work of Dr. Fownes has long been before the 
public, and its merits have been fully appreciated as 
the best text-book on Chemistry now in existence. 
We do not, of course, place it in a rank superior to 
the works of Braude, Graham, Turner, Gregory, or 
Gmelin, but we say that, as a work for students, it is 
preferable to any of them.— Lond. Journal of Medicine. 












BLANCHARD & LEA’S SCIENTIFIC PUBLICATIONS. 


11 


JUST ISSUED. 

II L^Bloxa C m C < Wifh F l E R IISTRY ’ 7 hPoretica J’ Practical - and Technical. By A. F. Abel, F. C.S., and C. 
' „ | ' , , . a Becommend>*iory Preface by Dr. Hofmann, and numerous illustrations on wood. In 

one large and handsome octavo volume, offi62 pages, extra cloth. 

a I InilfcM unde r ood ffiat this is a work fitted for the earnest student, who resolves to pursue for himself 
‘vljfi U chemical mysteries of creation. For such a student the “ Handbook” will prove an 
{ • • ° t r e \ Since ae Wl m no1 merely the most approved modes of analytical investigation, but 

kiofj ,. !!!■,, apparatus necessary, with such manipulatory details as rendered Faraday’s Chemical 
J i l0 .!' S . 50 valuable at the time of its publication. Beyond this, the importance of the work is in¬ 
creased by the introduction of much of the technical chemistry of the manufactory.— Atlienceum. 


xT the principal forms of the skeleton, 

, D , THE FORMS AND STRUCTURE OF THE TEETH. By Professor R. Owen. In one very 
handsome royal l2mo. volume, with numerous illustrations on wood. (Just Issued.) 

This volume will present in a concise and popular form a complete view of the most recent state of com¬ 
parative osteology; the correctness of which is sufficiently vouched for by the name of the distinguished 
author. A subject of so much interest to the man of science, and more especially to the geologist, cannot 
tail to attract general attention. 


TECHNOLOGY; 

OR. CHEMISTRY APPLIED TO THE ARTS AND TO MANUFACTURES. By Dr. F Knapp. Edit- 
e( 1.,with numerous Notes and Additions, by Dr. Edmund Ronalds and Dr. Thomas Richardson. With 
additional Notes by Prof. Walter R. Johnson, lit two large and very handsome octavo volumes, with 
about five hundred splendid illustrations. 

PRINCIPLES OF THE MECHANICS 

OF MACHINERY AND ENGINEERING. By Prof. Julius Weis bach. Translated and edited by Prof. 
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octavo volumes, with about one thousand beautiful illustrations. 


CARPENTER ON A LCO H O L-(J U ST ISSUED.) 

ON THE USE AND ABUSE OF ALCOHOLIC LIQUORS IN HEALTH AND DISEASE. By W. B. 
Carpenter, M. D., author of “ Human Physiology,” Ac. New edition, with Preface and Notes, by D. F. 
CoxDtE, M. D. In one neat royal 12ino. volume, extra cloth. 

This new edition has been prepared with a view to an extended popular circulation of this valuable work, 
the notes by Dr. Condie containing explanations of the scientific terms employed. Copies in flexible cloth 
may be had Iree of postage by mail on remitting 50 cents to the publishers. 

A very liberal deduction will be made when quantities are taken for distribution by societies or individuals. 

DE LA BECHE’S GEOLOGY. 

THE GEOLOGICAL OBSERVER. By Sir Henry T. De la Beche, C. B., F. R. S , Direcior-Genera; of the 
Geological Survey of Great Britain. In one large and handsome octavo volume, extra cloth, of seven 
hundred pages, with over three hundred wood-cuts. 

This volume will be found to present a very complete summary of what has already been accomplished 
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future researches should be pursued. 

BONAPARTE’S AMERICAN ORNITHOLOGY. In four handsome quarto volumes, with large and 
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BRODERIP’S ZOOLOGICAL RECREATIONS. In one neat royal 12mo. volume, extra cloth. 
BOWMAN’S HANDBOOK OF PRACTICAL CHEMISTRY, including Analysis. In one neat royal 
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BEALE ON THE LAWS OF HEALTH IN RELATION TO MIND AND BODY. A Series of Letters 
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GRIFFITH’S CHEMISTRY OF THE FOUR SEASONS, Spuing, Summer, Autumn, and Winter. In 
one handsome volume, large royal 12tno., with many wood-cuts. 

BUSHNAN’S POPULAR PHYSIOLOGY 

OF ANIMAL AND VEGETABLE LIFE. In one handsome royal 12mo. volume of200 pages, with over 
100 engravings on wood. (Now Ready.) See p. 9. 


PHYSICAL GEOGRAPHY. 

Bv Mary Somerville. A new American, from the last and Revised London Edition. With Notes and a 
Glossary, by \V. S. W. Rusciienberger, M.D., U.S. N. In one large royal 12mo. volume, extra cloth, 

(See p. 2.) 


DANA ON ZOOPHYTES AND CORALS. Being a portion of the scientific publications of the U.S. 
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colored plates, handsomely and strongly bound in half morocco. 

EVANS’S YOUNG MILLWRIGHT’S AND MILLER’S GUIDE. Fourteenth Edition. Edited by Thomas 

P Jones In one octavo volume, leather, with numerous plates. 

GREGORY’S LETTERS TO A CANDID ENQUIRER ON ANIMAL MAGNETISM. In one large 
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HUMBOLDT’S ASPECTS OF NATURE IN DIFFERENT LANDS AND DIFFERENT CLIMATES. 

Translated by Mrs. Sabine. In one large royal 12mo. volume, extra cloth. 

HALE’S ETHNOGRAPHY AND PHILOLOGY OF THE UNITED STATES EXPLORING EXPE¬ 
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THOMSON’S DOMESTIC MANAGEMENT OF THE SICK ROOM. In one large royal 12mo. volume, 

LARDNER'S NATURAL PHILOSOPHY AND ASTRONOMY. In three very large royal 12mo. vols., 
of 2000 pages, with 1000 illustrations. JJ^r* See p. 3. . 

QCHfFni FR’S BOOK OF NATURE. A Popular Introduction to the Sciences of Physics. Astronomy, 
S ChSry, MineVaVogyV Geology. Botany, Physiology, and Zoology. In one large crown octavo volume, 

with nearly 700 illustrations. ILr* See p. 4. 














12 BLANCHARD & LEA’S MISCELLANEOUS PUBLICATIONS. 

COMPLETE LIBRARY EDITION. 


LIVES OF THE QUEENS OF ENGLAND, 

FROM THE NORMAN CONQUEST: 

WITH ANECDOTES OP TIIEIR COURTS. 

Now first published from Official Records, and other Authentic Documents , Private as well as Public. 


NEW EDITION, WITH ADDITIONS AND CORRECTIONS. 

13Y AGNES STRICKLAND. 


Complete in six very handsome crown octavo volumes, containing over tiitrty-six hundred 
pages, and for sale in various styles of binding, at very reasonable prices. 


The publishers have great pleasure in presenting to the public this work in a complete fbrm. 
During,the long period in which it has been issuing from the press, it has assumed the character 
of a standard work, and as occupying ground hitherto untouched; as embodying numerous his¬ 
torical facts heretofore unnoticed, and as containing vivid sketches ol the characters and manners 
of the times, with anecdotes, documents, &c. &c., it presents numerous claims on the attention 
of both the student of history and the desultory reader. 


A valuable contribution to historical knowledge. 
It contains a mass of every kind of historical matter 
of interest, which industry and research could col¬ 
lect. We have derived much entertainment and in¬ 
struction from the work.— AtliencEum. 

This interesting and well-written work, in which 


the severe truth of history takes almost the wild¬ 
ness of romance, will constitute a valuable addition 
to our biographical literature .—Morning Herald. 

These volumes have the fascination of a romance 
united to the integrity of history.— Times. 


Also, to be had separate, 

STRICKLAND’S LIVES OF THE QUEENS OF HENRY VIII., and of his Mother, ELIZA¬ 
BETH OF YORK. Complete in one very neat crown octavo volume, extra cloth, of over four 
hundred pages. 

STRICKLAND’S MEMOIRS OF ELIZABETH, Second Queen Regnant of England and Ireland. 
Complete in one very neat crown octavo volume, extra cloth, of nearly six hundred pages. 


INTRODUCTORY VOLUME TO THE QUEENS OF ENGLAND—(Just Issued.) 

LIVES OF THE QUEENS OE ENGLAND 

BEFORE THE NORMAN CONQUEST. 

BY MRS. MATTHEW HALL. 

Complete in one handsome crown octavo volume, various styles of binding, to match 

Miss Strickland’s Work. 

This book, embracing a period anterior to that selected by Miss Strickland, becomes a neces¬ 
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match, and in every way uniform in style. 


HISTORY OF THE PROTESTANT REFORMATION IN FRANCE. By Mrs. Marsh, author 
of “Two Old Men’s Tales,” &c. In two very handsome royal 12mo. volumes, extra cloth. 

PULSZKY’S MEMOIRS OF AN HUNGARIAN LADY. In one neat royal 12mo. volume, 
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PARDOE’S COURT AND TIMES OF FRANCIS I., KING OF FRANCE. In two handsome 
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LORD HERVEY’S MEMOIRS OF THE COURT OF GEORGE II. In two neat royal 12mo. 
volumes, extra cloth. 


RUSSEL’S LIFE OF FOX—(Just Issued ) 


MEMORIALS AND CORRESPONDENCE OF 

CHARLES JAMES FOX. 


Edited by the Rt. IIon. Lord JOHN RUSSEL, M. P. 
In two handsome royal 12mo. volumes, extra cloth. 


The work is deeply interesting, as it throws light 
upon the career of a great man, and reveals the pri¬ 
vate sentiments of many eminent British statesmen 
in regard to our revolutionary struggle, and in regard 
to the wars waged against the. French Republic. 
The correspondence presents Mr. Fox in the attitude 
of a friend to the colonies, not only on general prin¬ 
ciples, but as one whose feelings were strongly en¬ 


listed in their cause. There are occasional letters in 
these volumes, which, if they had fallen into the 
hands of the British government at that time, would 
probably have caused the author some trouble, though 
it was a period when parly spirit ran very high, 
and statesmen took the largest license.—A. Y. Com¬ 
mercial Advertiser. 













BLANCHARD & LEA’S MISCELLANEOUS PUBLICATIONS. 13 


Campbell’s Chancellors and Chief Justices. 

LIYES OP THE LORD CHANCELLORS 

3lnb Keepers of ti)c ©recit Seal of (England, 

FROM 

THE EARLIEST TIMES TO THE REIGN OF KING GEORGE IV. 

BY LORD CHIEF-JUSTICE CAMPBELL, A.M., F. R. S. E. 

Second American, from the Third London edition, 

COMPLETE IN SEVEN HANDSOME CROWN OCTAVO VOLUMES, EXTRA CLOTH, OR HALF MOROCCO. 


ALSO, TO MATCH. 

LIYES OF THE CHIEF-JUSTICES OF ENGLAND, 

From the Norman Conquest to the Death of Lord Mansfield. 

Second Edition. 

In two very neat volumes, crown octavo, extra cloth, or half morocco. 


Of the solid merit of the work our judgment may be 
gathered from what has already been said. We will 
add, that from its infinite fund of anecdote, and happy 
variety of style, the book addresses itself with equal 
claims to the mere general reader, as to the legal or 
historical inquirer; and while we avoid the stereo¬ 
typed commonplace of affirming that no library can 
be complete without it, we feel constrained to afford it 
a higher tribute by pronouncing it entitled to a distin¬ 
guished place on ihe shelves of every scholar who 
is fortunate enough to possess it.— Frazer's Magazine. 


A work which will take its place in our libraries 
as one of the most brilliant and valuable contribu¬ 
tions to the literature of the present day.— Athenaeum, 

The brilliant successof this work in England is by 
no means greater than its merits It i< certainly the 
most brilliant contribution to English history made 
within our recollection; it lias the charm and free¬ 
dom of Biography combined with the elaborate and 
careful comprehensiveness of History.— N. Y. Tri¬ 
bune. 


ON THE LAW OF CONTRACTS, 

AND ON PARTIES TO ACTION EX CONTRACTU. By C. G. Addison, of the Inner Temple, 
Barrister at Law. In one large and handsome octavo volume. 


A NEW LAW DICTIONARY, 

Containing Explanations of such Technical Terms and Phrases as occur in the wotks of Legal^ 
Authors, in the Practice of the Courts, and in the Parliamentary Proceedings of the Houses ot 
Lords and Commons. To which is added an Outline of an Action at Law, and of a Suit in 
Equity. By Henry James Holthouse, Esq. Edited, from the second and enlarged English 
edition, with numerous Additions, by Henry Penington, of the Philadelphia Bat. In one 
large royal 12mo. volume, of live hundred double-columned pages. 


TURKEY AND ITS DESTINY. 

BY CHARLES MACFARLANE, ESQ. 

In two neat royal 12mo. volumes, extra cloth. 


NIEBUHR’S ANCIENT HISTORY. 

LECTURES ON ANCIENT HISTORY: 

COMPRISING 

The fflstory of the Asiatic Nations, the Egyptians, Creeks, Macedonians, and Carthaginians. 

BY B. G. NIEBUHR. 

Translated from the German, by DR. L. SCHMITZ, 

WITH ADDITIONS FROM MSS. IN THE EXCLUSIVE POSSESSION OF THE EDITOR. 

In three very handsome crown octavo volumes, extra cloth. 

fhmiliaritv of Niebuhr with the literatures of all nations, his profound know- 
The extraordin. y • ‘ ^ affairs derived not only from books, but from practical life, and 

ledge of all in these Lectures, a’s in those on Roman history, 

his brilliant power startling conceptions and opinions, as are rarely to be met with 

such an abundance of new,deas start g im J, ortance am , interest to all who arc engaged in 

ridt-ronA J!.W. of any period' in the history of man. 















14 BLANCHARD & LEA’S MISCELLANEOUS PUBLICATIONS. 


NARRATIVE OF THE UNITED STATES EXPEDITION 


TO TIIE DEAD SEA Aft’D RIVER JORDAN. 

BY W. F. LYNCH, U.S.N., 

Commander of the Expedition. 


In one very large and handsome octavo volume with twenty-eight beautiful plates, and two maps. 


This book, so lon^ and anxiously expected, fully 
sustains the hopes of the most sanguine and fastidious. 
It is truly a magnificent work. The type, paper, 
binding, style, and execution, are all of the best and 
highest character, as are also the maps and engrav¬ 
ings. It will do more to elevate the character of 


'our national literature than any work that has ap¬ 
peared for years. The intrinsic interest of the sub¬ 
ject will give it popularity and immortality at once. 
It must be read to be appreciated; and it will be 
read extensively, and valued, both in this and other 
countries.— Lady's Book. 


Also, to be had— 

CONDENSED EDITION, in one neat royal 12mo. volume, extra cloth, with a map. 


MEMOIRS OF THE LIFE OF WILLIAM WIRT. 

By tiie IION. JOHN P. KENNEDY. 

SECOND EDITION, REVISED. 

WITH A PORTRAIT, AND FAC-SIMILE OF A LETTER FROM JOHN ADAMS. 

In two large and handsome royal 12mo. volumes, extra cloth. 

In its present neat and convenient form, the work is eminently fitted to assume the position 
which it merits as a book for every parlor-table and for every fireside where there is an appre¬ 
ciation of the kindliness and manliness, the intellect and the affection, the wit and liveliness 
which rendered William Wirt at once so eminent in the world, so brilliant in society, and so 
loving and loved in the retirement of his domestic circle. Uniting all these attractions, it cannot 
fail to find a place in every private and public library, and in all collections of books for the use of 
schools and colleges, for the young can have before them no brighter example of what can be ac¬ 
complished by industry and resolution, than the life of William Wirt, as unconsciously related by 
himself in these volumes. 


DON QUIXOTE DE LA MANCHA. Translated from the Spanish of Miguel de Cervantes 
Saavedra, by Charles Jarvis, Esq. Carefully revised and corrected, with a Memoir of the Au¬ 
thor and a notice of his works. With numerous illustrations, by Tony Johannot. In two beau¬ 
tifully printed volumes, crown octavo, various styles of binding. 

The handsome execution of this work, the numerous spirited illustrations with which it abounds, and the 
very low price at which it is offered, render it a most desirable library edition for all admirers of the immortal 
Cervantes. 


NARRATIVE OF TIIE UNITED STATES EXPLORING EXPEDITION. By Charles Wilkes, 
U. S. N., Commander of the Expedition. In six large volumes, imperial quarto. With several 
hundred illustrations on steel and wood, and numerous large maps. Price $60. 

This is the same as the edition printed for Congress. As but few have been exposed for sale, those who 
desire to possess this magnificent monument of the arts of the United States, would do well to secure copies 
without delay. 


PICCIOLA, THE PRISONER OF FENESTRELLA ; OR, CAPTIVITY CAPTIVE. By X. B. 
Saintine. New edition, with illustrations. In one very neat royal 12mo. volume, paper 
covers, price 50 cents, or extra cloth. 


YOUATT AND LEWIS ON THE DOG. 

THE DOG. By William Youatt. Edited by E. J. Lewis, M.D. With numerous and beautiful 
illustrations. In one very handsome volume, crown 8vo., crimson cloth, gilt. 


YOUATT AND SKINNER ON THE HORSE. 

THE HORSE. By William Youatt. A new edition, with numerous illustrations ; together with 
a general history of the Horse ; a Dissertation on the American Trotting Horse; how trained 
and jockeyed y an Account of his Remarkable Performances ; and an Essay on the Ass and the 
Mule. By J. S. Skinner, Assistant Postmaster-General, and Editor of the Turf Register. In 
one handsome octavo volume, extra cloth, with numerous illustrations. 

This edition ofYouatt’s well-known and standard work on the Management, Diseases, and Treatment of 
the Horse, has already obtained such a wide circulation throughout the country, that the Publishers need 
say nothing to attract to it the attention and confidence of all wlio keep Horses or are interested in ilietr im¬ 
provement. 

THE GARDENER’S DICTIONARY. 

A DICTIONARY OF MODERN GARDENING. By G. W. Johnson, Esq. With numerous ad¬ 
ditions, by David Landreth. With one hundred and eighty wood-cuts. In one very large royal 
12mo. volume, of about 650 double-columned pages. 

The work is now offered at a very low price. 


THE LANGUAGE OF FLOWERS, with Illustrative Poetry. To which are now added Hue 
Calendar of Flowers, and the Dial of Flowers. Ninth American, from the Tenth London edi¬ 
tion. Revised by the editor of “ Forget-me-Not.” In one elegant royal 18mo. volume, extra 
crimson cloth, gilt, with beautiful colored plates. 


















BLANCHARD & LEA’S MISCELLANEOUS PUBLICATIONS. 


15 


GUIZOT’S CROMWELL—(Lately Issued.) 


HISTORY OF OLIYER CROMWELL 

AND THE 

ENGLISH COMMONWEALTH, 

FROM THE EXECUTION OF CHARLES I,, TO THE DEATn OF CROMWELL, 


BY M. GUIZOT. 

Translated by ANDREW R. SCOBLE. 

In two large and handsome royal 12mo. volumes, extra cloth, containing over 900 pages. 


To such a work as Mr. Guizot has here assigned 
himself he is eminenlly competent. Erudite, labori¬ 
ous, and accurate ; familiar alike with the facts that 
constitute the bones and the flesh and the blood of 
history, and the motives that give them vitality; at 
once free from the zealotry of the bigot and the indif- 
ferentism of the mere philosopher ; bound to no parti¬ 
sanship and pledged to no theories ; he has enjoyed 
the advantages of knowledge, impartiality, and clear¬ 
sightedness. and the result is a faithful portrait of the 
times, animated with a wise and truthful spirit, and 


showing in all its colors and touches the hand of a 
skilful master .—Philadelphia North American. 

We cannot doubt that this important work will 
meet with a hearty and universal welcome. The 
position of M. Guizot, the circumstances of bis coun¬ 
try, and the interest of his theme, will combine to at¬ 
tract towards his “ History of Cromwell” no ordinary 
share of public curiosity. No Englishman could have 
handled this subject with more effect, and M. Guizot 
adds new and valuable matter to our history.— Athe- 
nceum. 


BUFFUM’S SIX MONTHS IN THE GOLD MINES; from a Journal of Three Years’Residence 
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MACKAY’S WESTERN WORLD, or Travels in the United States; exhibiting them in their 
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TRAVELS IN SIBERIA, including Excursions Northward, down the Obi to the Polar Circle, and 
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HUNGARY AND TRANSYLVANIA, with Remarks on their condition, Social, Moral, and Po¬ 
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GRAHAME’S UNITED STATES. 

HISTORY OF THE UNITED STATES, from the Plantation of the British Colonies till their 
Assumption of Independence. Second American edition, enlarged and amended, with a Me¬ 
moir by President Quincy, and a Portrait of the author. In two very large octavo volumes, 
extra cloth. 


HISTORICAL SKETCH OF THE SECOND WAR BETWEEN GREAT BRITAIN AND THE 
UNITED STATES. By Charles J. Ingersoll. Vol. I. embracing the events of 1812-13. 
Vol II. the events of 1814. Octavo. 

MIRABEAU; a Life History. In Four Books. In one neat volume, royal 12mo., extra cloth. 

HISTORY OF TEN YEARS, 1830-1S40; OR, FRANCE UNDER LOUIS PHILIPPE. By 
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HISTORY OF THE FRENCH REVOLUTION OF 1789. By Louis Blanc. Vol I., crown Svo., 
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HISTORY OF THE HUGUENOTS. A new edition, continued to the present time. By W. S. 
Browning. In one octavo volume, extra cloth. 

HISTORY OF THE JESUITS, from the Foundation of their Society to its Suppression by Pope 
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with their Revival and Present State. By Andrew Steinmetz. In two handsome volumes, 
crown 8vo., extra cloth. 


WILLIAM PENN: 

* vt HISTORICAL BIOGRAPHY, from new sources; with an extra Chapter on the “ Macaulay 
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1C BLANCHARD & LEA’S MISCELLANEOUS PUBLICATIONS. 


P 

THE PEOPLE’S ENCYCLOPEDIA. 

NECESSARY TO EVERY SCHOOL AND TOWNSHIP LIBRARY. 

THE ENCYCLOPEDIA AMERICANA; 

A POPULAR DICTIONARY OF 

ARTS, SCIENCES, LITERATURE, HISTORY, POLITICS, BIOGRAPHY; 

INCLUDING 

A COPIOUS COLLECTION OF ORIGINAL ARTICLES IN AMERICAN BIOGRAPHY; 

On the basis of the seventh edition of the German Conversations-Lexicon. 

Edited by FRANCIS LIE BE R, 

ASSISTED BY 

E. WIGGLESWORTII and T. G. BRADFORD. 

With Additions, by Professor HENRY VETHAKE, 

Of the University of Pennsylvania. 

Complete in fourteen large octavo vols., containing nearly nine thousand double-columned pages. 

FOR SALE IN VARIOUS STYLES OF BINDING, AT EXCEEDINGLY LOW PRICES. 

This work is so well and so favorably known to the public, that the publishers feel it unnecessary 
to adduce any of the encomiums which have been bestowed on it from all quarters. As a copious 
library for constant and ready reference, on all subjects connected with the past and present state 
of mankind, and on every branch of human knowledge and attainment, it presents great advantages 
to all who are unable to accumulate large collections of books, containing in itself, as it does, vast 
stores of information, on almost every topic on which information can possibly be sought, from the 
simplest questions of history or statistics, to the most complex points of science or criticism. The 
steady demand which still continues for it, notwithstanding the immense number of copies which 
have been circulated, sufficiently proves the necessity of such a work for all educated men, and the 
thorough satisfaction which it continues to give to all who consult its pages; and shows that the 
publishers have not miscalculated in bringing the work up to a late period, with notices of con¬ 
temporary events and persons, while reducing the price to about one-half of the original subscription. 


Tlie Illustrated Geographical Encyclopcedia. 

THE ENCYCLOPAEDIA OF GEOGRAPHY; 

Comprising a complete description of the Earth, Physical, Statistical, Civil, and Political. Exhi¬ 
biting its Relation to the Heavenly Bodies, its Physical Structure, the Natural History of each 
Country, and the Industry, Commerce, Political Institutions, and Civil and Social State of all 
Nations. By Hugh Murray, F. R. S. E., &c. Assisted in Botany, by Professor Hooker—Zoolo¬ 
gy, &c., by W. W. Swainson—Astronomy, &c., by Professor Wallace—Geology, &e., by Pro¬ 
fessor Jameson. Revised, with Additions, by Thomas G. Bradford. In three large octavo 
volumes, containing about nineteen hundred large imperial pages, and illustrated by eighty- 
two small Maps, and a colored Map of the United States, after Tanner’s ; together with about 
eleven hundred Wood-cuts, executed in the best style, and representing every variety of object, 
curious either in Nature or Art. Remarkable Buildings; Views of Cities; Places celebrated in 
History, or interesting from Natural Phenomena; the Appearance and Customs of the various 
Nations; Objects in Natural History, Birds, Beasts, Fishes, Shells, Minerals, Insects, Flowers, 
Plants, Utensils, Objects of Commerce ; in short, everything which engages the curiosity or 
industry of man enters into the scope of this Encyclopaedia, and is here seen, described, and 
figured. 

The manner in which these multifarious subjects have been treated by the Editor and his able 
coadjutors has afforded universal satisfaction; and the style in which it is presented to the Ame¬ 
rican public, though at a cost comparatively trifling, is worthy of the exalted reputation of the work. 


ACTON’S COOKERY. 

MODERN COOKERY IN ALL ITS BRANCHES, reduced to a System of Easy Practice, for the 
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minute exactness. By Eliza Acton. With numerous wood-cut illustrations; to which is 
added a Table of Weights and Measures. The whole revised, and prepared for American house¬ 
keepers, by Mrs. Sarah J. Hale. X 8 7 second London edition. In one large 12mo. vol. 

#v_i2 c - ■'» " • * m 

FLETCHER’S NOTES FROM NINEVEH, AND TRAVELS IN MESOPOTAMIA, ASSYRIA, 
AND SYRIA. In one neat royal 12mo. volume, extra cloth. 

BAIRD’S IMPRESSIONS AND EXPERIENCES OF THE WEST INDIES AND NORTH 
AMERICA. In one neat royal 12mo. volume, extra cloth. 

READINGS FOR. THE YOUNG, from the works of Sir Walter Scott. In two very handsome 
royal lSmo. volumes, with beautiful plates. 

SMALL BOOKS ON GREAT SUBJECTS : a Series of F.ssays, by a few' Well-Wishers to Know¬ 
ledge. In three neat royal ISmo. volumes, extra cloth. 























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